WEBVTT

1
00:00:21.345 --> 00:00:24.210
WH11NE- Sunrise: Please ticket.

2
00:00:34.910 --> 00:00:38.820
WH11NE- Sunrise: or can between zoom hear me? Okay, perfect.

3
00:00:39.970 --> 00:01:01.810
WH11NE- Sunrise: So let me just get started. So Hi, everyone my name is Akash. I'm currently a postdoc at the Accelerator Division. I finished my Phd. About 2 years ago on, in fact, this exact same topic, which was to be very new to me, and I was offered a postdoc here, which I was glad to accept, because now I get to

4
00:01:01.810 --> 00:01:13.909
WH11NE- Sunrise: see it through, because we have some exciting time ahead. And yeah, thanks for this opportunity to, you know. Invite me to this Forum. Talk to you all.

5
00:01:14.458 --> 00:01:43.969
WH11NE- Sunrise: So there was. There are 2 ways that I could have structured this talk. One would be to just directly jump into the intricacies of the beam physics, the nonlinearity of it, and the finer details of what we call as a restaurant extraction, and then and then, just, you know, speed on with it. But I understand that not everyone in the audience could be our experts in accelerator physics. So I thought

6
00:01:44.100 --> 00:02:04.540
WH11NE- Sunrise: this could be a good opportunity for me to talk about accelerator physics and a little about fermilab accelerator complex, and then slowly build to the nonlinear beam physics process that goes into beam delivery from U to B. There are 2 disclaimers that I would like to say. One is that

7
00:02:04.670 --> 00:02:22.510
WH11NE- Sunrise: since this is going to be a whirlwind introduction to accelerator physics, there's going to be a lot of hand waving. But what I would like to get from it is just the essence of the beam physics concepts that we want to talk about. And I'm not going to talk about all the systems

8
00:02:22.510 --> 00:02:34.699
WH11NE- Sunrise: that go into beam delivery, only the ones that are pertinent to this and that, too, not in that great of a detail, but it would hopefully. It stands as a good introduction. In case you want to learn something later, you can always do that?

9
00:02:35.282 --> 00:02:41.687
WH11NE- Sunrise: So so yeah, let's start the further ado to set up the stage.

10
00:02:42.320 --> 00:03:08.360
WH11NE- Sunrise: so mu 2 e this, as if you may know, is an upcoming experimented formula that intends to look for a charged electron flavor violation. And the way mu 2 E intends to do that is, to take a muon, and then shoot the muon inside an aluminum atom, and then store the aluminum atom in the sorry store, the muons in the aluminum atoms, Coulomb field nucleus coulomb field and then wait for the mu to decay.

11
00:03:08.410 --> 00:03:35.189
WH11NE- Sunrise: If we have a direct conversion of Muon to electron without any neutrinos, then we expect the energy of the decayed, the electron product from the decayed muon to have almost the rest mass of the muon. There is some energy that goes into the nuclear binding energy and the nuclear recoil energy. But more or less, we know what energy of electron that we have to look for. And the way

12
00:03:35.260 --> 00:03:50.090
WH11NE- Sunrise: we create the these Muons is by bombarding proton pulses on to a muon production target. And then you take the backscattered muon. You transport it, and then you hit this muon into aluminium stopping target. And then you have the experiment.

13
00:03:50.320 --> 00:03:57.010
WH11NE- Sunrise: Now there are some significant background processes for this experiment that hinders our measurement.

14
00:03:57.350 --> 00:04:05.179
WH11NE- Sunrise: So this direct conversion is not strictly prohibited by standard model, but it's extremely suppressed to the order of 10 power, minus 50 or something like that.

15
00:04:05.270 --> 00:04:28.060
WH11NE- Sunrise: The previous experiment called syndrome, 2. Then at Tsi it used almost the same technique, but it used gold atoms, and the bound they set were about 10 bar, minus 13. But Mu. 2 intends to reach a sensitivity of a better of about 4 orders of magnitude to about 10 bar minus 19, and one of the significant background processes is what is called a radiative ion capture.

16
00:04:28.060 --> 00:04:56.279
WH11NE- Sunrise: So as these, the protons hit the Muons gets produced, and along with the Muons some pions also come for the right. And there is a process that would happen in which the pion can interact with the nucleus, and it can produce a gamma, the photon. And this gamma and another gamma could interact and produce electron positron. And this electron produced from this interaction could mimic the Mu 2 E electron which we do not want.

17
00:04:56.360 --> 00:05:14.209
WH11NE- Sunrise: So in order to circumvent that what mu 2 we cleverly does is you shoot the muon inside the aluminum atom, and whatever secondary, the secondaries that come with it. But you don't start the live window of data recording. So you wait until all these background electrons fly away.

18
00:05:14.210 --> 00:05:29.870
WH11NE- Sunrise: and after that you have the live window where you look for mu to v electrons, and then the next set of muons come. So what this right away tells you is, you do not want a continuous stream of Muons to come, but you want pulses of Muons to come.

19
00:05:30.090 --> 00:05:35.990
WH11NE- Sunrise: If you want pulses of nuance. What that. What that means is you need to create pulses of protons.

20
00:05:36.240 --> 00:06:04.310
WH11NE- Sunrise: And how do we get those pulses of protons? So that's going to be the main story behind. At least this talk, which makes the beam to be possible. So just a quick number. So this waiting window is almost 700 nanoseconds, which means it would be ideal to have a pulse to pulse duration of about 1.6 microseconds in order for the experiment to work efficiently.

21
00:06:04.910 --> 00:06:07.143
WH11NE- Sunrise: Okay, this is the setup.

22
00:06:07.660 --> 00:06:35.359
WH11NE- Sunrise: And now the question is, how do we get these proton pulses to go? Yes, you said, I mean, okay, it's a 700 nanosecond window. Is that determined by the physics? And then you match the beam to the physics, or is it that's determined by the beam dynamics of you can get this. I mean time it into this. It's an excellent question. It's a happy coincidence of both. Yes, so, in fact, when the beam delivery schemes were being investigated for this.

23
00:06:35.690 --> 00:06:50.550
WH11NE- Sunrise: Also, we're considering other machines to deliver the beam from. But as I'm going to show the the delivery ring happens to be a really good candidate for that. And it's exactly because of this temporal structure that it could give. So yeah, good question.

24
00:06:50.930 --> 00:07:06.079
WH11NE- Sunrise: Okay, so now let's have a quick, you know, run through of the Fermi accelerator complex. One thing I would like to say is a lot of the stuff that we're going to see now, halfway through the talk and also the accelerator physics concepts.

25
00:07:06.090 --> 00:07:22.969
WH11NE- Sunrise: They are not centered just to formula, but it can be. The concepts are applicable even to other machines, especially to Lhc. That's very close and dear to your heart. So, but there could be some technical caveats here and there, but regardless it could be a good introduction to have

26
00:07:23.762 --> 00:07:28.789
WH11NE- Sunrise: so this is the overall fermi accelerator, fermilab accelerator complex.

27
00:07:29.272 --> 00:07:36.699
WH11NE- Sunrise: So let's quickly go through each of these. Now, I'm not talking about many of the accelerators here.

28
00:07:36.750 --> 00:07:54.880
WH11NE- Sunrise: because they have not written into Mu 2 V. But these are the accelerators that we do need to provide beam to mu 2. V. So let's just go to the very 1st step, which is the ion source, and it good. You can see the cursor. So it all starts over here.

29
00:07:54.910 --> 00:08:08.749
WH11NE- Sunrise: So what the ion source does is so we have about 2 bottles of hydrogen, essentially is where the story starts, and the hydrogen is then provided with an arc, and a plasma is formed.

30
00:08:08.750 --> 00:08:27.359
WH11NE- Sunrise: and then this plasma has h plus ions, and then we have a cathode, a molybdenum cathode coated with some cesium because the cesium decreases the work function of the molybdenum. And this shoots out electron and the electron that shoots out sticks to these h plus ion. What we want is

31
00:08:27.360 --> 00:08:45.910
WH11NE- Sunrise: h minus ions, and once enough time is given for this h minus ions to be created. We then pulse these anode in such a way that we give about a voltage offset of 35 kilovolts, such as the h minus ions, shoot out

32
00:08:45.910 --> 00:08:59.130
WH11NE- Sunrise: at 35 kb, so you may ask, why catch minus ions? Why not directly start with protons? We'll see why it's actually a clever reason. So once the

33
00:08:59.140 --> 00:09:10.699
WH11NE- Sunrise: once it comes out, then we pass it through some solenoids to to give it some focus, and it passes through this anzel lens. So what this lens does is, it acts as a beam chopper, so it gives

34
00:09:10.760 --> 00:09:25.399
WH11NE- Sunrise: almost a 35 kilovolt of potential opposite to it. So as the pulse comes in, it accumulates, and then it's let go, and then you have a train of these hedge minus ions let through. So it it kind of acts as a beam chopper.

35
00:09:25.850 --> 00:09:33.620
WH11NE- Sunrise: And then this 35 Kv beam H minus ions. Enter this thing called radio frequency quadrupole. So what this Rf, Q does is

36
00:09:33.760 --> 00:09:51.290
WH11NE- Sunrise: it provides transverse focusing. We're going to see more about what that means shortly, and it also gives some longitudinal focusing as the pulse comes through, it gives some longitudinal time structure to it, and then it accelerates it to about 750 kev.

37
00:09:51.410 --> 00:10:05.220
WH11NE- Sunrise: and then the H. Minus ions are passed through these quads, and also further punching, and we have 750 Kv. H. Minus ions, coming out of this ion source in the earlier days prior to 2,012. Instead of this Rfq.

38
00:10:05.250 --> 00:10:30.969
WH11NE- Sunrise: We had this Cockcroft and water generator. In fact, this was constructed when Fermilab was constructed. In fact, it was bought from a 3rd party vendor in the 19 seventies. In fact, the 1st director founding Director Wilson. He was so fond of this Cockroft water generator that so, in fact, if you see, there is a man standing there just to give you a sense of scale. He wanted to keep this

39
00:10:31.010 --> 00:10:45.190
WH11NE- Sunrise: generator right in the middle of Wilson hall. Just so people can see, and people can be inspired aesthetically. The the physicist who was working with the group called Donald Young. Some of the old timers here may perhaps remember so he

40
00:10:45.440 --> 00:11:04.740
WH11NE- Sunrise: permanently opposed to it, and Wilson again, being a very strong character, he was like, no, no, we should do this, and Donald had threatened to resign, because if you have this right in the center of Wilson Hall, then there has to be a 90 degree bend in the Limac, and that's such a risky thing to have as a starting point for your whole lab

41
00:11:04.740 --> 00:11:29.389
WH11NE- Sunrise: that Donald Yang told. Hey, this is the case. Then I'm out. And then, Wilson conceded, and we did sadly. We do not have this at the center of Wilson Hall, but if you, in fact, walk out the Wilson Hall, and if you go to the Linac starting point, I don't know if your Id card hopefully it does. You can actually see this Cockroft Water generator. You don't know which party can access and which party you can't. So you can. You can

42
00:11:29.390 --> 00:11:35.069
WH11NE- Sunrise: take some shifts, and so you can just go across with with, you can go across and you can walk through

43
00:11:35.070 --> 00:11:41.360
WH11NE- Sunrise: perfect. That's nice. Maybe we'll do a tour with you, maybe. Yeah, sure. Absolutely.

44
00:11:41.748 --> 00:11:59.221
WH11NE- Sunrise: So yeah, there is that story. It's decommissioned now. Right? Yes, it is decommissioned. So we can move it. There are there 2 of them actually also, Ethan. To my knowledge there is one I don't know if there is a spare stored somewhere. But

45
00:11:59.760 --> 00:12:09.820
WH11NE- Sunrise: but yeah, I I know that when they were building the lab, a lot of attention went into the main ring focus. So in fact, Wilson was okay to just buy this

46
00:12:09.900 --> 00:12:32.339
WH11NE- Sunrise: from a 3rd party vendor. And it's some. I think this was brought in from Sweden or something, and, in fact, another factor is the Ion source, and the Van de Graaff and the Linac is an exact copy of Brookhaven National Lab. In fact, Brookhaven National Lab Commission, and then, 12 days later, Fermilabs Linac Commission. So it was almost a twin of both.

47
00:12:34.240 --> 00:12:39.149
WH11NE- Sunrise: Okay, 15 min already. Okay, I'm gonna go into some digressions. But they are interesting.

48
00:12:39.590 --> 00:13:07.150
WH11NE- Sunrise: Okay, now, okay, just continue the story. So we have 750 Kv hitch minus ions coming out, and now they are fed into Linux. Linux, as you may know, is a linear accelerator. So this was again built as a part of the initial construction at formula, and our Linux has about 2 sections to it. The 1st section is called a drift tube, Linux. We have 5 drift tubes.

49
00:13:07.150 --> 00:13:16.949
WH11NE- Sunrise: and the second is called an side coupling accelerator. I don't expect to know what that is, but but one- one cool thing to know about the rift tube Linux. So these

50
00:13:17.140 --> 00:13:30.680
WH11NE- Sunrise: the drift tubes. So this whole thing that you see there's an accelerator cavity and these drift tubes, in fact, are covered in alternative voltages. So what happens is

51
00:13:30.840 --> 00:13:34.420
WH11NE- Sunrise: as the particle enters into this drift tube

52
00:13:34.896 --> 00:13:45.329
WH11NE- Sunrise: the electric field. So what we want is the particle to experience a longitudinal electric field for it to accelerate. So the particle accelerate. But of course, at some point the electric field flips

53
00:13:45.450 --> 00:13:57.499
WH11NE- Sunrise: when the electric field flips, because it's oscillatory, you don't want the particle to experience, and the electric field is negative, as it will start to decelerate. So what happens here is as the particle enters into the drift tube, it acts as a Faraday cage.

54
00:13:57.500 --> 00:14:25.279
WH11NE- Sunrise: and the particle does not feel the opposite electric field anymore, and by the time the particle comes out it gets attracted towards the next drift tube. But now the acceleration is the right direction. So this is choreographed in a way that the particle accelerates every time when it's in between 2 drift tubes. So we have about 5 drift tube tanks, and it is accelerated to from 750 kev to about 1 16 Mev. So here this cartoon is a little

55
00:14:25.430 --> 00:14:40.310
WH11NE- Sunrise: too hand wavy, like everyone, so I'm not going to go into the details of where, exactly in this peak you want the particles to reside. Is it left or right? It's an interesting question, but we won't have time to cover that. But if you want, you can look up later.

56
00:14:40.830 --> 00:14:54.169
WH11NE- Sunrise: And then, okay, so it comes out and it the. It's then accelerated to about 400 Mav. At the end of the Lenac, and we have 400 Mev. H. Minus ions coming out of the Linac.

57
00:14:54.330 --> 00:14:59.979
WH11NE- Sunrise: and then it's fed into this circular thing called the booster.

58
00:15:00.030 --> 00:15:13.600
WH11NE- Sunrise: So this booster is what we call a synchron machine. I'll explain what it is. So when one question you may have is, well, it's h minus that's entering. When does it get converted to protons?

59
00:15:13.600 --> 00:15:32.809
WH11NE- Sunrise: And it happens just before the particles enter into this booster. So this line in the top that you see are circulating h plus ions, which is a nickname for protons, the one that you see from the bottom. Here is the 400 Mev. H. Minus ions that come from the Lenac.

60
00:15:32.820 --> 00:15:40.149
WH11NE- Sunrise: and this is one of the main reasons why we use H minus ions instead of protons, and this because, as the H. Minus ions enter.

61
00:15:40.270 --> 00:15:43.979
WH11NE- Sunrise: you see that the the h plus and h minus

62
00:15:44.140 --> 00:15:48.730
WH11NE- Sunrise: gets bent by the same magnetic field, but they get bent in the opposite direction.

63
00:15:48.990 --> 00:16:04.439
WH11NE- Sunrise: and now they are merged and they pass through this vertical strip. It's a carbon strip, and this carbon strips off the 2 electrons from the H minus ion, and once it comes out, it you have protons.

64
00:16:04.630 --> 00:16:08.130
WH11NE- Sunrise: and and the electrons, you know, get lost in the scattering.

65
00:16:08.230 --> 00:16:09.010
WH11NE- Sunrise: If

66
00:16:09.080 --> 00:16:29.180
WH11NE- Sunrise: you have h minus ions that were not stripped, you have again a magnetic field in this region. Now they kick the h minus ions and h plus ions in different directions. And now the H minus ions are dumped into this dump here, and the h plus continues to circulate in the booster. So we have this

67
00:16:29.250 --> 00:16:40.770
WH11NE- Sunrise: clever technique of splitting. And then the whatever protons that continue to circulate in the booster continues to do so, and the incoming h minus ions get stripped into protons, and they just to join the booster

68
00:16:41.633 --> 00:16:45.899
WH11NE- Sunrise: and then, once you fill up the booster.

69
00:16:46.040 --> 00:16:59.799
WH11NE- Sunrise: and then what you do is now you have protons in the booster. Now these are 400 mev protons, and you accelerate those 400 mev in a synchronous fashion to 8 Gb.

70
00:16:59.920 --> 00:17:28.360
WH11NE- Sunrise: And then, as you do that, in fact. So there are Rf. Cavities within this booster, and these Rf. Cavities provide some longitudinal structure to the beam. So once the proton enters. So the protons kind of fill up the whole booster. Once you switch on the Rf cavity because of the frequencies that are chosen between the revolution frequency and the Rf. Frequency. These protons in the booster get

71
00:17:28.390 --> 00:17:33.670
WH11NE- Sunrise: seg, get segmented into about 80 or so different pulses.

72
00:17:33.820 --> 00:17:51.040
WH11NE- Sunrise: and then, once you have, that you then accelerate these 80 pulses to 8 gev. And then you eject, and then you inject into this thing called the recycler. So the recycler, then, is the second largest accelerator

73
00:17:51.070 --> 00:18:16.079
WH11NE- Sunrise: physically at formula. Right now it's the largest operating accelerator in the lab, so the recycling ring is made of permanent magnets which can support 8 Gb. Protons. This was constructed earlier during the teletron days to help with the production of the antiprotons, but now it was reconfigured to store. I mean it is configured to store protons to deliver beam to the Muon campus.

74
00:18:16.980 --> 00:18:27.579
WH11NE- Sunrise: So the 8 Gb. So remember that from when- when the when the beam exits the booster, it segments it's segmented into 80 plus or so pulses.

75
00:18:27.990 --> 00:18:47.620
WH11NE- Sunrise: Once it's injected into the recycler, there is the Rf system inside the recycler that regroups these 80 trains of pulses into 4 big pulses, and the intensity of this is about 4 times 10 power 12 protons that's circulating with one time 10 power, 12 proton in each of those pulses.

76
00:18:47.780 --> 00:19:05.989
WH11NE- Sunrise: and this proton. These proton pulses are then sent to the delivery ring. The muon delivery ring right now. This, of course, was used to aid 2 experiments, the G minus 2 and the mu 2 v. Right now G minus 2 is done during the G minus 2 days this

77
00:19:06.190 --> 00:19:23.119
WH11NE- Sunrise: delivery ring, which is a triangular ring, it's about 500 meters in circumference. It was used to store the Muons, and then those Muons were sent to the G minus 2 storage ring. But now we have repurposed this delivery ring to store protons.

78
00:19:23.200 --> 00:19:51.119
WH11NE- Sunrise: and this delivery ring is where the action is going to happen for mu, 2 be so. The goal for the mu 2 E beam delivery is to inject about one E. 12 protons into this delivery ring, and over the course of the next. You know some finite number of turns to extract a uniform slice of these protons, and then send to this green line, which is called the M. 4 beam line and send to the Mu 2 E

79
00:19:51.280 --> 00:19:56.699
WH11NE- Sunrise: building the motivate target hub. So the target lies at the end of this opposite 14 line.

80
00:19:56.860 --> 00:19:57.560
WH11NE- Sunrise: So

81
00:19:58.460 --> 00:20:01.330
WH11NE- Sunrise: Now, how do we do this

82
00:20:01.520 --> 00:20:16.889
WH11NE- Sunrise: split? How do we extract a uniform slice of the circulating beam. That's a tricky question. And again, there is a clever way of how we intend to do it. And this is where nonlinear beam physics comes into play. So before we go into that, let's have

83
00:20:17.150 --> 00:20:23.170
WH11NE- Sunrise: a kind of a quick primer of accelerator physics. So

84
00:20:23.440 --> 00:20:34.929
WH11NE- Sunrise: what is accelerators? Well, you move particles from A to B typically charged particles. Not just that. Of course, you move particles from A to B with a specific energy in mind

85
00:20:35.190 --> 00:20:40.299
WH11NE- Sunrise: and not just with a specific energy. But you also want a specific energy and specific intensity.

86
00:20:40.770 --> 00:20:45.940
WH11NE- Sunrise: and not just that, because you also want a longitudinal time structure that you want with the beam

87
00:20:46.415 --> 00:21:10.570
WH11NE- Sunrise: and as you can guess, that's not enough, you need also something called a face space control and this directly relates with minimizing the beam losses. Now, I don't expect you to know what face spaces, but we'll we'll get to that shortly. This face space control and the minimum beam loss is going to be one of the most crucial things that's needed for the new beam delivery.

88
00:21:11.022 --> 00:21:29.647
WH11NE- Sunrise: There is another aspect, which is, you move particles from A to B with an existential angst. For when B is so far away, but sometimes you, it actually comes to your aid, because you have enough distance to manipulate the beam the way you want it to. But usually I would rather have it shorter.

89
00:21:30.300 --> 00:21:36.029
WH11NE- Sunrise: so this is kind of the overall goal, for you know, accelerator physics to to help achieve.

90
00:21:36.280 --> 00:21:43.939
WH11NE- Sunrise: And now we care about what degrees of freedom do we have when we look at a particle. So here the circle that you see here

91
00:21:44.050 --> 00:21:45.999
WH11NE- Sunrise: is the bean pipe.

92
00:21:46.200 --> 00:22:14.910
WH11NE- Sunrise: The X axis is the horizontal position of the particle, and the Y axis is the vertical position of the particle and the X cross y. The longitudinal direction is the cross product of these 2 coordinates. So this coordinate system is called frennet, 7 coordinate system. So this is a local coordinate system that travels along with the particle this way. It's useful to

93
00:22:14.920 --> 00:22:19.929
WH11NE- Sunrise: to look at how these quantities evolve. See if you have a stable beam or not.

94
00:22:20.210 --> 00:22:45.639
WH11NE- Sunrise: So what are the degrees of freedom? Well, it's the horizontal position of the particle. Now, as you see, we don't have just all the particles sitting exactly at the center of the beam. There's bound to be some distribution, but there is also a distribution in the angle of the particles, so each particle will have some random angle that it's pointed to, and both these are independent. Any particle can have any position in any angle, and same goes for the vertical as well.

95
00:22:45.690 --> 00:23:09.490
WH11NE- Sunrise: and the last 2 degrees of freedom are the momenta, or the energy of the particle, and also the arrival time of the particle. In other words, if you look the beam from the sideward as it's going, what does its temporal or longitudinal structure look like, and how is the energy distribution to the given particle? So these are the 6 main variables that we care about in accelerator physics.

96
00:23:09.490 --> 00:23:37.609
WH11NE- Sunrise: So for the purposes of this talk, we are mainly interested in transverse degrees of freedom, and all that means is just the plot that you see here and the angles of each particle. So you care about the horizontal plane and the vertical plane. In fact, in our case, for the resonant extraction. We care much more about the horizontal plane, because that's where particles get killed or extracted, or a lot of these things. Dynamics happen in the horizontal plane

97
00:23:37.790 --> 00:24:07.790
WH11NE- Sunrise: the angle here. Can you tell me exactly what angle from? Yeah. Good question. So you can see the angle here. Imagine the circle as a beam pipe that's coming right? Yeah. So each particle is not going to go obediently straight. Sure, it's going to go this way, this way, that way in the horizontal plane, and similarly, the vertical plane. It would have any random angle. So the angle that is coming from in the yes, exactly. You were just talking about the coordinates traveling with the with the V

98
00:24:07.790 --> 00:24:08.859
WH11NE- Sunrise: right? Yes.

99
00:24:09.800 --> 00:24:16.629
WH11NE- Sunrise: So with respect to the the central. Okay, yeah. In fact, there's a plot that I would show, but not here. But

100
00:24:17.180 --> 00:24:45.839
WH11NE- Sunrise: this angle is, with respect to the ideal design trajectory of the part. So, accelerator, let's say it's a perfect circular accelerator. So you have a predefined ideal circular trajectory, but each particle locally within the circumference is not going to have the exact circle. It's going to locally have some angles. And if you don't do anything, it's just going to get lost, actually. So that's why there are other interesting things that ways in which you can contain the beam. But yeah, good question.

101
00:24:45.950 --> 00:24:50.890
WH11NE- Sunrise: So, yeah, these are the 4 main transfers, degrees of freedom that we care about.

102
00:24:51.650 --> 00:24:54.519
WH11NE- Sunrise: And these are the main players

103
00:24:54.740 --> 00:25:15.689
WH11NE- Sunrise: that we use to manipulate the beam in the transverse direction in the longitudinal direction. There are a lot of cavities that you use. But for this talk we are not going to touch about that. And all fields that I talk about are going to be magnetic under the wave stated, because, like, you know, for high energy particles.

104
00:25:15.730 --> 00:25:25.489
WH11NE- Sunrise: The magnetic force thankfully, is proportionate to its velocity. So we make use of that. I mean, for example, in the delivery ring. This

105
00:25:26.240 --> 00:25:45.410
WH11NE- Sunrise: the Strangler ring that I sort of talked about where the action happens. These bending fields that you see for 8 Gv. Proton. The magnetic field that you require is, I think, something like a calculus per point 3 dust or something. But if you replace that with electric field, it's about a hundred 1 million volts per meter

106
00:25:45.410 --> 00:26:05.470
WH11NE- Sunrise: just ridiculously high, if you know, I mean, the air breaks down at 3 million volts per meter. Lightning is like 10 kilovolts per meter. So we do not have that. So maybe in accelerated prophysics, especially high energy machines, we make use of magnetic fields. There is a component of electric field that would come in into our picture. But I'll tell you that later when we get there.

107
00:26:05.800 --> 00:26:29.540
WH11NE- Sunrise: Okay, so let's quickly go through each of these elements. So dipole. Of course, everyone knows just a uniform magnetic field. So typically this, this is how a typical dipole looks like. So we would have coils that run in the top and bottom, and, as you know, the ampere tells you that when you have a current that goes around you will have a magnetic field.

108
00:26:29.540 --> 00:26:55.599
WH11NE- Sunrise: and the coil below should also follow the same direction, else it would give it opposite beam, and it would cancel. But so this is how a typical magnetic field would look like. So you would have the beam pipe and the fields would penetrate through this beam pipe, and the particles would experience this magnetic field. So the dipole field typically gives a circular bend, and in some cases it also provides some weak focusing, even though now we're not going to that.

109
00:26:55.600 --> 00:27:03.522
WH11NE- Sunrise: And in the machines you also use the dipole fields to kick the beam into other accelerators. So sometimes,

110
00:27:04.020 --> 00:27:19.309
WH11NE- Sunrise: one accelerator would be in the ground floor. Other would be in the second floor, which means you'd have to kick the particle up. So you use these dipole fields to, you know, direct the particle upward, not just bend downward. So that's that's dipole for you.

111
00:27:19.610 --> 00:27:22.880
WH11NE- Sunrise: And the next important

112
00:27:23.040 --> 00:27:33.020
WH11NE- Sunrise: component. In fact, I would say the most important component is the quadrupole. So what this quadrupole does is it creates a magnetic field that's

113
00:27:33.330 --> 00:27:47.009
WH11NE- Sunrise: proportional to how far away you are from the center. So if you are in the dead center, like you can see all the, all the field lines cancel out, and there's nothing in the center. But if you just look at the horizontal plate, for example.

114
00:27:47.762 --> 00:27:49.969
WH11NE- Sunrise: The field strength increases

115
00:27:50.040 --> 00:28:14.970
WH11NE- Sunrise: as you deviate away from the ideal. X equals 0. So if a particle finds itself in the side away from the center, it experiences a restoring force towards the center. And that typically happens on the other side as well. If if the particle is negative or horizontal plane, then it also gets a restoring force towards the center.

116
00:28:15.030 --> 00:28:28.849
WH11NE- Sunrise: However, if you write down the Maxwell's equation, the curve of B equals 0, because the charge free origin. And you would find that if you, if the forces is restoring in one plane, it's actually blowing up in the vertical plane.

117
00:28:29.170 --> 00:28:34.330
WH11NE- Sunrise: so that that means that the particles the kick

118
00:28:34.540 --> 00:28:40.970
WH11NE- Sunrise: would be given for in a focusing way in the horizontal plane. But it would be defocusing in the vertical plane.

119
00:28:41.130 --> 00:28:46.849
WH11NE- Sunrise: So so what do you do? So what you do is you alternate the performance.

120
00:28:47.030 --> 00:29:10.199
WH11NE- Sunrise: So you put a focusing quad. So whatever particles that were not exactly in the center of the horizontal plane will get focused, but the vertical will get refocused, and then it exits, and there is just a drift region where there is no field, and then now it enters another quadrupole, but this quadrupole is flipped, so here the horizontal direction would get refocused, and the vertical will get focused.

121
00:29:10.370 --> 00:29:31.680
WH11NE- Sunrise: And then this cell is called a photocell. It's focused drift, defocused drift. So in any accelerator, even in the Lhc you would have these cells of photos, and if you keep these attached as a string together, you would have a stable beam throughout. And this is how you actually keep a stable beam.

122
00:29:33.950 --> 00:29:59.310
WH11NE- Sunrise: and then we have the 3rd actor, which is the 6th pole. This has 6 poles. So one thing that we see I told you that a particle would get a kick, a focusing kick in the quadrupole, but all magnetic forces are velocity dependent, and not all particles would have the same momentum, so each particle would have different momentum. So what that means is

123
00:29:59.420 --> 00:30:15.009
WH11NE- Sunrise: for a gate for the same quarter pole. Different particles would get focused to different extent, so they will not all get focused the same way. So in order to correct for this, you use the sector pole magnet. So the sextapole typically would focus

124
00:30:15.010 --> 00:30:33.469
WH11NE- Sunrise: the beam on one side, and it will defocus the beam on the other side. So what you do is you take these particles that do not have the same momentum, and you make it go through a bend. So as it goes through a bend, the particles that are higher, momentum will not curve as much. The particle with lower momentum will curve a lot.

125
00:30:33.490 --> 00:30:54.509
WH11NE- Sunrise: and then you bend them, and you put them in a straight position in a straight drift region. And now you have the particles separated in space where the higher momentum particles are one side and lower momentum particles on the other side, and when you do that, you make them pass through the sextapole, and the Sextopole will give more focus additional focus to these higher momentum particles, because they are more rigid

126
00:30:54.510 --> 00:31:06.030
WH11NE- Sunrise: and it would give less focus to the lower momentum particles. So this way, you actually can correct for this momentum dispersion within within a given beam. And this

127
00:31:06.030 --> 00:31:35.979
WH11NE- Sunrise: this phenomenon, where the focus is different for a different momenta. This is in a difference in something called a tune, which I will talk about shortly, and, as you can see here, if you have an optical lens, you know, a red light will have a different focal length than a blue light. So this even an accelerator physics we call this phenomenon a chromatic aviation. And typically you would have sextapoles to correct for this chromatic aviation. So if you hear an accelerator, physics talk about the chromatic sextipoles, this is what they mean

128
00:31:35.990 --> 00:31:39.750
WH11NE- Sunrise: just to focus different particles with different energy.

129
00:31:41.420 --> 00:31:44.680
WH11NE- Sunrise: Okay, so now we are dangerously close to

130
00:31:45.150 --> 00:31:57.929
WH11NE- Sunrise: right in the actual equations of motion. I'm not going to. I realize it's 1, 35 already. So I'm not going to go into the details of this. So this is the coordinate system that you asked about. So here

131
00:31:58.200 --> 00:32:10.450
WH11NE- Sunrise: we have the ideal trajectory, which is XDX design. But if you have a particle that's straight away, so the deviation from the ideal trajectory is denoted by X,

132
00:32:10.590 --> 00:32:17.869
WH11NE- Sunrise: and the deviation from the ideal tangent or slope is denoted by X prime. So X. Prime is actually the deviation from the ideal trajectory.

133
00:32:17.910 --> 00:32:46.070
WH11NE- Sunrise: So anyway, if you you know the Maxwell's equations, and you know the magnetic field. Sometimes the magnetic field is not a constant. It could be also X dependent, because a quarter pole. The more away you are the more kick the quadrupole would give you. So with all that in mind when you put in the gradient of the quadrupole, and or also a dipole. And then you solve in this coordinate system you get an equation that looks like this. So this is

134
00:32:46.120 --> 00:33:07.239
WH11NE- Sunrise: when you linearize it, because it's a. It's a good equation to linearize, because, just to give you a sense here, the row would be the radius of curvature for the particle accelerator. So that would be in the order of 100 meters, or I mean in in Lhcs in kilometers, right? But this X would be in in millimeters. Typically so sometimes it.

135
00:33:07.240 --> 00:33:31.570
WH11NE- Sunrise: It strikes me that we have all these buildings and all these infrastructure, and all that is for a beam that's like 1.5 like thick. So X is actually, very, very small. So these assumptions are very reasonable to make. So anyway, you get an equation of the evolution of this X in terms of the magnetic fields that you expose it to.

136
00:33:31.600 --> 00:33:42.990
WH11NE- Sunrise: and likewise you can also do for the the Y plane here and for Xplane. But you can do for y plane. So what we see here is almost a simple harmonic, like equation.

137
00:33:44.430 --> 00:33:48.389
WH11NE- Sunrise: So this, except there is one difference. So when I go back

138
00:33:49.050 --> 00:33:54.379
WH11NE- Sunrise: here it's it would be a simple harmonic equation if

139
00:33:54.610 --> 00:34:21.030
WH11NE- Sunrise: this B prime and B rho are constant throughout the accelerator. But that's not the case, it's constant for a given magnet at a given location. It's not constant throughout. So when I write this as a simple harmonic equation, the K of S is actually not a constant throughout the accelerator it is constant at a given location. So what this means is

140
00:34:21.310 --> 00:34:39.069
WH11NE- Sunrise: now you have a spring constant where you have simple harmonic oscillation. But the spring constant is not a constant, the spring constant is proportional to where it is being compressed, in which case you would have a very different in which the simple harmonic motion would be modulated by this change in the spring, constant

141
00:34:39.159 --> 00:34:51.360
WH11NE- Sunrise: but regardless. So now you have the evolution equation of of this X parameter. And now you can solve for a drift region. If you have no field at all, then K is simply 0,

142
00:34:51.360 --> 00:35:11.240
WH11NE- Sunrise: which means X double prime equals 0, which means X prime equals constant. So what that tells you is, if a particle is drifting in a field, free region, and if it has a non-zero angle, its X is going to deviate as it continues to go, so the deviation is directly proportional to how much distance it has traveled in this case. Here it's S.

143
00:35:11.630 --> 00:35:41.559
WH11NE- Sunrise: Now, if you have a gradient field like a focusing quad or defocusing quad, the evolution would. So here you see, in one plane it would be focusing. Here. You see, this is an oscillatory behavior, but in the other plane the sign would be different, and here you have the hyperbolic sine and cosine, in which case the beam would just blow up. But we saw how we tackle that you alternate the quads to give a sense. Okay, now that I have the equations for the evolution of X,

144
00:35:41.670 --> 00:35:44.390
WH11NE- Sunrise: and also for X prime, I can now.

145
00:35:44.490 --> 00:35:52.369
WH11NE- Sunrise: at the I can make a piecewise solution in an accelerator in an accelerator. If I have a bunch of quads, a bunch of dipoles, and a bunch of dirts.

146
00:35:52.430 --> 00:36:05.659
WH11NE- Sunrise: I know how the particle is going to behave before entering and after entering, because I know the equations of motion. And now I can make a transport matrix for this accelerator, and

147
00:36:05.660 --> 00:36:24.060
WH11NE- Sunrise: these would be the transport matrices. So L is the is the length of the of the particular magnet, and K would be the characteristic strength. It could be the dipole strength, or it could be the quadrupole strength and X and X prime. Sorry X. Naught and X prime 0

148
00:36:24.060 --> 00:36:35.969
WH11NE- Sunrise: are the initial coordinates, angle and position of the particle, so after it enters and exits the magnet, its position and angle would change. With respect to these equations. This couple linear equations.

149
00:36:37.060 --> 00:36:54.760
WH11NE- Sunrise: Okay? So now I have this. Now, I can then solve for design for whatever magnet that I want. So our interest is this accelerator called the delivery. And just for just to show you so I said in my tracking code, I just took a single particle.

150
00:36:55.020 --> 00:36:56.560
WH11NE- Sunrise: and I

151
00:36:56.700 --> 00:37:04.669
WH11NE- Sunrise: I circulated the single particle once around this delivery ring, and it came back to where it started, and I froze the simulation.

152
00:37:05.300 --> 00:37:14.829
WH11NE- Sunrise: Here I'm plotting the X evolution of the particle about the ideal 0 as it goes once around the ring.

153
00:37:14.890 --> 00:37:39.549
WH11NE- Sunrise: Now, the 1st thing that we notice is so, this X equals 0 is the ideal trajectory. But because this particle started with a non-zero position with not an ideal angle. It's not following the exact design trajectory. But it's oscillating about that ideal trajectory. Now this is a single particle. But if you imagine a bunch of particles, a lot of these are going to execute these oscillations, and this is called a Beta Tron oscillation.

154
00:37:39.600 --> 00:37:48.689
WH11NE- Sunrise: So you remember, we had a simple harmonic equation, but where the spring constant was not a constant, but a function of the position.

155
00:37:48.840 --> 00:38:03.469
WH11NE- Sunrise: So what I did here is I normalized that deviation of the spring constant and I divided that. And now we see that we have a pure sinusoid in these arbitrary units that I have denormalized that.

156
00:38:04.210 --> 00:38:20.299
WH11NE- Sunrise: And just like how you do the position. You can also plot the angle evolution again normalized. And you also expect that to to follow a sinusoid just like that did because it's a coupled linear equation system.

157
00:38:21.440 --> 00:38:22.260
WH11NE- Sunrise: Okay.

158
00:38:22.380 --> 00:38:32.019
WH11NE- Sunrise: Now, one thing that we see is if you count the peak. So we have 123-45-6789. We have about 9 peaks here.

159
00:38:32.300 --> 00:38:44.399
WH11NE- Sunrise: So what that means is a particle, is executing about 9 oscillations as it goes once around the line, so this oscillation is called the tune of an accelerator.

160
00:38:44.580 --> 00:38:54.109
WH11NE- Sunrise: The skew is an important parameter. Now, typically, you would want to avoid integer tubes, because if you have some error in a magnet somewhere.

161
00:38:54.110 --> 00:39:16.630
WH11NE- Sunrise: the particle is going to come exactly in that same position again and again. And it's going to experience that same error in the kick. And then it's going to get lost. So typically, you want to avoid this, what we call a resonance condition. But this is the design of the delivery ring. The magnet strengths are designed in such a way that the tune of the delivery ring a starting tune at least is 9.6 5 0.

162
00:39:17.520 --> 00:39:44.659
WH11NE- Sunrise: This is an important parameter. Now I started the particle somewhere, and then this particle has done execution, and then it has ended somewhere. So and then we can. The same has happened to the angles, too. So at the end of each turn you can note, like where the particle was and where the particle is right now, and you can plot the evolution of this angle and position, and that would be the phase, space, evolution of the particle.

163
00:39:45.380 --> 00:39:48.149
WH11NE- Sunrise: So here I'm making an animation

164
00:39:48.360 --> 00:40:15.010
WH11NE- Sunrise: at a single location where the particle is going. 100 turns. But I'm plotting the angle and the position of the particle to normalize, because I want it to be a circle, but we can see that it's not blowing away. It's executing oscillation about the x-axis, and the angle is also executing some oscillation about the y-axis, but it's stable. So one question. I told you that the tune is 9.6 5 0.

165
00:40:15.110 --> 00:40:34.640
WH11NE- Sunrise: So one question you could ask is, why are there the islands like this? Right? So if I quickly count, if I count star as one, so you have 1, 2, 3, 4, 5, 6, 7, 8, 9, 1011, 1213, 1415, 1617, 1819 20. There are about 20 islands here. Right? Why are there 20 islands?

166
00:40:35.280 --> 00:40:43.080
WH11NE- Sunrise: But that's because the tune of the machine is 9.6 5 0. Now, if you drop the integer part, which you don't care about.

167
00:40:43.230 --> 00:40:47.520
WH11NE- Sunrise: the fractional part is 0 point 6, 5 0, and that's exactly 13 by 20.

168
00:40:47.760 --> 00:40:58.810
WH11NE- Sunrise: So what this means is at every turn in the phase space, the particle is moving by an angle of 2 pi times 13 by 20,

169
00:40:59.410 --> 00:41:20.350
WH11NE- Sunrise: and that's about. And if you calculate in degrees, that's about 126 degrees. Now, if I go back to the animation. You can actually see the particle jumping about 120 degrees every time jumps. It's kind of pretty neat to see if you give enough time this particle would fill this circle, and then it will continue to just keep on doing this so long as the beam is stable.

170
00:41:20.720 --> 00:41:25.030
WH11NE- Sunrise: So. So now we are at a position where we can

171
00:41:25.490 --> 00:41:47.809
WH11NE- Sunrise: more than halfway into the talk. Get to the resonant extraction from U. 2 E. So. Yes, if you wanted to change that tuning, would that just come from the magnets that are affecting the exactly good question. Yeah, you. You foresee a lot of things. So it's it's the magnets that change the tune. And typically it would be the quarter poles that would change

172
00:41:47.810 --> 00:41:57.630
WH11NE- Sunrise: the skew if you want to change it right? The the photo that you were talking about earlier. Right? Yes. So sometimes that could be just dedicated quarter polls in the link, and you change it. Just

173
00:41:57.680 --> 00:42:09.620
WH11NE- Sunrise: those finite number of quadruples, because they, in fact, contribute to this oscillation. And you can change the the Hume by by controlling these quadruples, and that's very crucial for mu to vp delivery, and I'll tell you why.

174
00:42:10.120 --> 00:42:11.210
WH11NE- Sunrise: So.

175
00:42:11.470 --> 00:42:22.532
WH11NE- Sunrise: voila! We are here. So now you know what X is, what X prime is, what a phase space is, and how the particles phase space evolves as it goes around and round around the ring.

176
00:42:23.450 --> 00:42:46.040
WH11NE- Sunrise: what is nonlinear about this. So far we have not talked about any nonlinearity. Dipole and quadrupole. Both are linear forces. But now we are going to talk about the nonlinearity, the beam physics. So just as a quick recap. So we talked about all these. You know how the beam gets to the delivery ring. So the mutual for the mu to be about

177
00:42:46.160 --> 00:43:09.199
WH11NE- Sunrise: 10 times 10 times 12, one equal protons would be injected into the delivery ring, and then over the course of the next 25,000 turns. The goal is to slice a uniform portion of the circulating beam and then send it to the new experiment. That's the goal. Now, how would that be achieved? Well, this will be achieved

178
00:43:09.320 --> 00:43:30.459
WH11NE- Sunrise: through something called a resonant extraction. I'll tell you what that is. So. These are the beam parameters for this extraction, so extraction, in normal terms, is just the slicing of the beam, or this is also called as a slow spill in the title of the top spilling the beams. So the delivery ring has that the circumstance of the delivery ring

179
00:43:30.460 --> 00:43:47.810
WH11NE- Sunrise: and the energy of the protons are such that it's a happy coincidence that the revolution time period is about 1.6 9 microseconds. This is almost exactly what the new dream was. So every time a proton comes a bunch of proton comes.

180
00:43:47.910 --> 00:44:03.129
WH11NE- Sunrise: it's sliced and then sent to a pulse is sent, and by the time the next proton pulse comes the same proton pulse go once around and comes. It's about 1.6 9 microseconds, which is the the pulse temporal design that you really wants.

181
00:44:03.860 --> 00:44:17.720
WH11NE- Sunrise: and if you if you divide one e. 12 protons by 25,000 terms. That comes to about 4 e. 7 protons per given term. So each pulse are expected to have 4 E. 7 protons.

182
00:44:17.860 --> 00:44:20.809
WH11NE- Sunrise: Okay, how? How does this spill happen?

183
00:44:20.980 --> 00:44:30.409
WH11NE- Sunrise: Now? Here I'm again plotting the angle in the Y axis and x-axis. Just the position of the beam, and here we are looking at the horizontal profile of the beam.

184
00:44:30.540 --> 00:44:51.470
WH11NE- Sunrise: If you don't have any sex, topole any nonlinear, if you have just dipoles and quadrupoles, just like I showed you earlier. The trajectory of these particles would simply be circles and nothing else. Now let us say that I switch on sextapoles. Something magical happens now Sextopole is turned on. So here I'm plotting every 3 turns.

185
00:44:51.570 --> 00:44:54.329
WH11NE- Sunrise: You see that all of a sudden, in the face space.

186
00:44:54.470 --> 00:45:02.430
WH11NE- Sunrise: We have some triangularity introduced because of the sextable field and with the successful field.

187
00:45:03.090 --> 00:45:31.860
WH11NE- Sunrise: You remember I also told you about the tune of the beam. So this tune, right now, here is about 9.6 5 8. Now, what happens if I switch on this extrapole? But then move the tune closer to a 3rd integer tune. So, for example, the closest 3rd integer to 658 is 6, 6, 6, 6, that's like 29 by 3. Right? So if you have the sex to poles on, and if you move the tune closer and closer to 6, 6,

188
00:45:32.280 --> 00:45:38.539
WH11NE- Sunrise: this is what happens. So some. A triangular region is all of a sudden present in the face space.

189
00:45:38.670 --> 00:45:56.999
WH11NE- Sunrise: If the particles inside the triangle it's stable. But see what happens when it comes, just comes out. This is going to be now and then boom, it just becomes nonlinear, and its position keeps on increasing forever and ever. So this happens because of the nonlinearity of the sex to pole field

190
00:45:57.060 --> 00:46:17.929
WH11NE- Sunrise: and the way the rate at which you squeeze this triangle is the rate at which you approach the resonant tube from 9.6 5 8 to 6, 6, 6. And the way you do that is as follows, so we have about 3 fast ramping quadrupoles. So quadrupoles change the tune like I mentioned

191
00:46:18.170 --> 00:46:40.690
WH11NE- Sunrise: the Sixtapoles that are there to excite this triangle. In the 1st place, we have about 6 of them 6 harmonic sextuples in the delivery ring, and both of these provide this magic in the phase space whereby it introduces a stable triangular region, and any particle that's outside this triangle their amplitude would increase every turn.

192
00:46:40.960 --> 00:46:45.299
WH11NE- Sunrise: and once the particles amplitude increases past

193
00:46:45.320 --> 00:47:04.499
WH11NE- Sunrise: certain magnitude. So here it's past 12 so we had, and in the delivery we have a location where we have an electrostatic septar. So imagine that in the beam pipe and at the septum location the particles are going around and round, and I introduce this restaurant condition. So the horizontal phase space

194
00:47:04.500 --> 00:47:20.589
WH11NE- Sunrise: is going to start blowing up in a controlled fashion, and whatever particle whose amplitude lies past the septa, this septum will give a kick horizontal kick to the particle, and just that portion of the beam will be sliced, and will be sent away to the Mutaway experiment.

195
00:47:20.720 --> 00:47:25.690
WH11NE- Sunrise: So this happens, turn by turn by turn by term. So, in other words, the rate

196
00:47:26.170 --> 00:47:29.619
WH11NE- Sunrise: at which you squeeze the triangle

197
00:47:30.000 --> 00:47:54.109
WH11NE- Sunrise: depends is directly proportional to the number of particles that you would extract at a given location. So so here, for example, I have a blue beam in which I have a horizontal tune of 9.6 5 0, which I talked about. If you, if you start the simulation. If you don't have any Sixtapoles, and if you remain in this tune, all these particles would just execute circular motion in this field.

198
00:47:54.150 --> 00:48:05.529
WH11NE- Sunrise: But if I switch on this extrapole, and as I go from 6, 5, 0 to 6, 6, 6, magically, a triangle happens, and all these particles that are that are branching out

199
00:48:05.740 --> 00:48:26.540
WH11NE- Sunrise: have just found themselves outside the stable region, and then they increase in amplitude and at a given location. We have a sector that's standing that gives a kick and it gets the unstable particles get extracted. And this is the way in which the beam is delivered to the new 2 E target. And this comes with a lot of

200
00:48:27.062 --> 00:48:50.679
WH11NE- Sunrise: problems. But yes, if you would have more sector, could you start the beam in different position and more? Yes, you can. Yes, but if you have, if you extract in different positions, you would have to dig different tunnels and different buildings. And you know, that's like not efficient, but for the G minus 2 experiment. We do not have the sector. In fact, there are

201
00:48:50.680 --> 00:49:09.489
WH11NE- Sunrise: type of kickers which kick the beam into a separate beam line which sent to the G. Minus 2 storage building. But in this case we have to put in a septum to direct it to the building. But in principle you are right. It doesn't matter where you keep the septurn, the delivery link, but it's going to extract where we keep it. So, yeah, good question.

202
00:49:11.370 --> 00:49:30.230
WH11NE- Sunrise: Okay, we are 152. So I want to end the talk by actually showing you some real data which is nice and exciting. But there are a bunch of diagnostic tools that we have when we have to do beam studies. One such thing is called a beam position monitor.

203
00:49:30.230 --> 00:49:47.409
WH11NE- Sunrise: So here we have 2 plates. We have plate A and plate B, and we have the beam going in between these 2 plates. What the Bbm does. Is it measures transversely where the beam is between these 2 plates, as you can imagine. If the beam is close to one plate.

204
00:49:47.410 --> 00:50:00.830
WH11NE- Sunrise: more charges will be induced in that plate as against the other, and you can find this difference in signal, and you can then convert that into a position of where the beam exactly is. Now, if the beam is exactly at the center, of course

205
00:50:00.870 --> 00:50:18.420
WH11NE- Sunrise: equal amount of charges would be induced on both the plates, and you would have 0 rating in the Dpm. But regardless, you can also find the intensity of the beam by summing up all the charges that are induced in both the plates, so you can get both intensity as well as where the beam is.

206
00:50:18.500 --> 00:50:22.540
WH11NE- Sunrise: So when I say team, I should be capturing what exactly we mean

207
00:50:22.730 --> 00:50:33.699
WH11NE- Sunrise: beam is just a bunch of charged particles. So what does this measure? This measures the centroid of the beam here it does not measure where the individual particles are, but it just measures the centroid.

208
00:50:34.110 --> 00:50:48.189
WH11NE- Sunrise: So using this, we can actually make some measurements. So in the delivery ring there are about more than 50 horizontal atms. So during the before the last shutdown, I was able to get some data. So here

209
00:50:48.350 --> 00:51:01.340
WH11NE- Sunrise: is the raw Bpm data that you that you see, and you can actually see the particles are oscillating about X equals 0. So before this, I should, I should say that because you measure the center of the beam

210
00:51:01.640 --> 00:51:24.580
WH11NE- Sunrise: before the beam is injected into the delivery ring. We gave a kick to the beam, so that the centroid itself is displaced from the center, because if the centroid was at the center, you just get 0 readings in the Bbm, because that's not what we want. But if you want to see the behavior of how the whole beam profile, you know, oscillates about the ring. You give a displacement or kick to it. So here I have plotted

211
00:51:24.868 --> 00:51:33.509
WH11NE- Sunrise: the individual data turn by turn data. So I've plotted about 80 turns. So one thing that we see here is because we are so close to the 3rd

212
00:51:33.510 --> 00:51:47.870
WH11NE- Sunrise: integer resonance. We see 3 sinusoids in the Bpm. In the beam oscillation, and it's it's pretty pretty so, and this is in millimeters. But you'll have to be careful in calibrating these things. But anyway, what I want to do is

213
00:51:47.920 --> 00:51:51.219
WH11NE- Sunrise: I know that there are many Ppms in the room.

214
00:51:51.320 --> 00:52:02.800
WH11NE- Sunrise: and I know the magnet strength in this delivery. What that means is, if I know the position of the beam in in the X of the beam in position one and x of the beam in position 2.

215
00:52:02.870 --> 00:52:22.209
WH11NE- Sunrise: And I know the magnets in between. Then I can actually mathematically calculate what the angles should be because I know the mattresses right, and if I do that, what do we see? So remember earlier. So if you have a sextapole and the closest goes close to 30 digit. You should see triangles, and I wanted to see if we do see triangles

216
00:52:22.310 --> 00:52:24.499
WH11NE- Sunrise: and voila. Do you see a triangle?

217
00:52:24.690 --> 00:52:41.060
WH11NE- Sunrise: So this is an actual data taken from the Bbm. It is so exciting for me to see this triangle because I did my Phd. For failures and simulations and everything, and I know the math. But you know, it's a totally different feeling when you actually see the beam. And yeah, it's something very gratifying.

218
00:52:41.290 --> 00:52:46.053
WH11NE- Sunrise: Oh, and another thing. Okay, we are very close. And another thing I want I want to leave you with is

219
00:52:46.480 --> 00:53:12.299
WH11NE- Sunrise: another measurement. So this measurement was done at the extraction line. So this device, this diagnostic tool, is called a wall current monitor. So what this does is. Again, this has 2 plates, and as the beam is entering and exiting. We have an image current that is induced on these plates, so, as the beam goes through, the current also passes in the wall.

220
00:53:12.420 --> 00:53:35.670
WH11NE- Sunrise: and you and you can then measure how fast this current goes, and you can convert that into the longitudinal structure of the beam. So the Bpm. Measures where the particle is transversely, but a wall current monitor is able to measure it longitudinally, which is nice. Just one day before the last shutdown, I was able to hook up with the scope

221
00:53:35.740 --> 00:54:00.729
WH11NE- Sunrise: and to a wall current monitor. So here I show you the extraction beam. So the beam enters, and one a 12 protons circulate, and each slice each turn it goes. A slice of these protons are extracted and sent into this green line. This is the extraction line. So we have a wall current monitor in this spot in the extraction line. So I want to see if we are indeed extracting protons. And this

222
00:54:00.820 --> 00:54:11.610
WH11NE- Sunrise: this, the wall, connect monitor data. So I sampled this at about 500 megahertz, which means every 2 nanoseconds. I'm sampling it. Well, what do you see? You don't see much, but if you

223
00:54:11.760 --> 00:54:14.620
WH11NE- Sunrise: zoom in, you see some pulses.

224
00:54:15.040 --> 00:54:16.910
WH11NE- Sunrise: and if you zoom in even further.

225
00:54:17.080 --> 00:54:20.540
WH11NE- Sunrise: you see these ulses. So these are individual proton buzzes

226
00:54:20.680 --> 00:54:26.473
WH11NE- Sunrise: that are extracted and being sent to W. 2 Ep. Now each of these pulses

227
00:54:27.330 --> 00:54:42.810
WH11NE- Sunrise: we ideally. We expected to have about one e. 7 protons in them. But right now we are in a commissioning phase. So we have a lot of other things to take care of the the extraction. Intensity is not strictly uniform, but again, it was so awesome to see

228
00:54:43.120 --> 00:54:57.989
WH11NE- Sunrise: protons. This is the 1st time I saw protons in real life, I mean in the plot. But but it's still, you know, it was pretty awesome. Okay? So it's 1, 57. So I kind of structured this talk. Okay, one thing I would like to end with this.

229
00:54:57.990 --> 00:55:27.859
WH11NE- Sunrise: You can do a Fourier transform on this full waveform. So you can actually see that there are some spikes. You know that these vertical lines that you see are artifact of amplifiers. You can ignore that. But you see the waveform itself kind of oscillates, and you see the baseline also kind of oscillates. And so I was curious as to what are the frequencies that contribute to this. So I just overnight ran in this powerful into Mac Fourier transform of these 15 million data points.

230
00:55:27.910 --> 00:55:56.479
WH11NE- Sunrise: And these are the results of the Fourier data points. And the horizontal is the frequency. And then I've plotted for reference the 60 Hertz harmonics, the 60 Hertz harmonics are the power supply. So it's so awesome that in the extracted proton pulses you see these power supply ripples that are there. So which means that we have a lot of noise in the extracted beam, and we, in fact, have something called a spill regulation system, which

231
00:55:56.610 --> 00:56:13.790
WH11NE- Sunrise: has the different components to it. To minimize these variations in the proton pulses that are extracted so that the mutability has uniform, because if you extract more protons, you would have, you know, detectable flash, you'll have deconstruction inefficiencies and stuff like that. So this.

232
00:56:13.870 --> 00:56:39.290
WH11NE- Sunrise: in fact, for for my Phd, this was my main focus. How to extract these with the uniform pulses. And now we are kind of seeing it through by implementing it in the hardware, and in fact, they may have been in the next few weeks, or I hope I'm not jinxed it. But but we are going to continue the commissioning studies. But anyway, I think this is like as good a place as any, because I just wanted to leave you guys with a sense of you know what being physics about? And

233
00:56:39.690 --> 00:56:50.739
WH11NE- Sunrise: So the between delivery and also the formula, accelerated, complex. And a lot of these things also transfer to the Lhc, so anyway, yeah, let me end this here. Thank you for your attention.

234
00:56:56.040 --> 00:56:58.090
WH11NE- Sunrise: We have questions.

235
00:56:58.580 --> 00:56:59.250
WH11NE- Sunrise: Okay.

236
00:56:59.520 --> 00:57:15.910
WH11NE- Sunrise: maybe you said for the resident extraction. What's the main benefit, or what's is there a different way? You do the extraction that you prefer not to use? For this or so? There are 2 ways that you can do resident extraction. So one is

237
00:57:16.400 --> 00:57:17.760
WH11NE- Sunrise: so. It depends on

238
00:57:18.130 --> 00:57:24.989
WH11NE- Sunrise: so all magnets can exert rustlings. If you use a quarter pole, the tune will not be 1 3, rd but it will be one half.

239
00:57:25.100 --> 00:57:45.390
WH11NE- Sunrise: so you could do half integer extraction. So, in fact, from the main injector to the switchyard. They do this thing called half integer extraction, whereby, over the course of 4 seconds, these 1 point integer protons are extracted and sent to the screen. But for us, when we did the analysis, it looked like 3rd integer was

240
00:57:45.530 --> 00:58:04.329
WH11NE- Sunrise: the way to go. Even in 3rd indigit extraction. There are 2 ways in which you can squeeze the triangle right one. So one is to just keep the Sextopole strength constant and move the tune closer to 2 thirds, or you keep the tune constant, but you just ramp up the sextupole string.

241
00:58:04.693 --> 00:58:26.149
WH11NE- Sunrise: There are different ways. You can do this. But again, this is given the beam, stability, and so on and so forth. I guess the the scheme of keeping the 6 to post in constant but ramping up the tune was the was the ideal one, but we do have option to play with it and see which configuration would work the best. But what makes a 3rd better than a half.

242
00:58:26.580 --> 00:58:53.259
WH11NE- Sunrise: It has to do with the lattice of the machine. What magnets there are already in the machine. So, in fact, there was also an investigation done to do 3rd integer extraction in the main injector. But I believe the magnets and the phase advance of the particles are not optimal enough that you could do that there. So a large factor also comes with what you already have and what you can do with a given machine.

243
00:58:53.430 --> 00:58:54.490
WH11NE- Sunrise: Yeah, good question.

244
00:58:56.260 --> 00:59:10.769
WH11NE- Sunrise: My question is maybe a variation on that, which is what is, why do this, which seems a bit more delicate compared to using a kicker magnet, a kicker magnet. Yeah, yes. So with a kicker magnet.

245
00:59:11.530 --> 00:59:17.830
WH11NE- Sunrise: it's hard to you. You would incite coherently all of all parts of the behavior.

246
00:59:18.040 --> 00:59:21.500
WH11NE- Sunrise: So it's it's hard to excite just the fringe border.

247
00:59:21.630 --> 00:59:40.490
WH11NE- Sunrise: if you just want part of the beam. Yes, just drawing a whole bits of it of it at a time. The whole thing exactly. Did you say you do use a kicker also? So you you induce this instability, and then you still use a kicker to abstract? Exactly so. In fact, if you if you if you see here

248
00:59:40.640 --> 00:59:43.590
WH11NE- Sunrise: so this it's in September.

249
00:59:43.730 --> 01:00:04.280
WH11NE- Sunrise: So the beam is coming in in this direction. So there is a cathode that's there behind these foils, and there is a strong electric field that it gives. So whatever particle is on the other side gets the kick, and it gets, and it gets like extracted on the other side. So this is, this is electrostatic kicker.

250
01:00:04.370 --> 01:00:24.760
WH11NE- Sunrise: But yeah, there are a lot of things also that you need to be careful with, because this guy has a finite thickness, we want it to be 50 microns, because if if it's even more thicker. Whatever beam comes in, it could also get lost in this, and it could cause radiation and stuff like that. But as this is a scheme we have. This is the electrostatic kickoff that kicks the beam and sends to mute

251
01:00:24.870 --> 01:00:31.800
WH11NE- Sunrise: one more silly, maybe stupid part. So in the face space, I don't have a good intuition for this, I mean, are you?

252
01:00:31.950 --> 01:00:37.369
WH11NE- Sunrise: Yeah, you're having the 3. If

253
01:00:37.770 --> 01:00:52.799
WH11NE- Sunrise: you're losing particles in 3 different parts of face space. Right? You're extracting in only one. Exactly. So good question. So let me use this cursor. Okay, let's let let me go back here so that we have a bigger image.

254
01:00:57.350 --> 01:01:12.000
WH11NE- Sunrise: okay, so here we have a space space. Right now, let us say that a particle is outside the triangle right? Now turn by turn. Its amplitude is going to increase. Okay, so what happens is at Turn one. It is in this, this arm

255
01:01:12.270 --> 01:01:36.199
WH11NE- Sunrise: in turn 2. It goes to this arm, but the radius is a little higher, and that it comes to the 3rd arm with even higher amplitude, and it jumps between these arms. But you extract at a single arm, right? So that single arm happens to be, yeah, yeah, that single arm happens to be whenever the particle falls on this side of the center which eventually it will happen. Yeah.

256
01:01:37.230 --> 01:01:53.720
WH11NE- Sunrise: yeah. Good question, does this extraction scheme gives you better extension between houses because you have more controls? Good question. I have not at all talked about extension. So if we go to the very 1st slide

257
01:01:53.860 --> 01:01:58.109
WH11NE- Sunrise: to zoom out. So we have the the live window right?

258
01:01:58.586 --> 01:02:23.829
WH11NE- Sunrise: Which means, there can't be pulses. So we have one proton pulse and another proton pulse. We should not have anything in between. So we have a system called extension system, which is a separate system which will kick off any particles that would come in between these things, so that that system is separately different. But yes, it's very crucial that that we have that. And and we do have that. So

259
01:02:25.040 --> 01:02:51.999
WH11NE- Sunrise: so whatever you extract, you still have to clean the protons in between the pulses. Yes, exactly, yes, and they do get kicked off by this thing called A/C dipole. So in the extraction line there is a dipole kicker which comes active especially within these 2 pulses, and it ramps down when the proton pulse comes. So you have that extinction. You give that kick to whatever stray protons that will come in between these 2 pulses.

260
01:02:53.391 --> 01:03:03.110
WH11NE- Sunrise: So how long do you keep the beam, you know, before before you have to dump it

261
01:03:03.330 --> 01:03:08.220
WH11NE- Sunrise: the design right now, the the spill time you inject one equal protons

262
01:03:08.390 --> 01:03:16.449
WH11NE- Sunrise: over the course of the next 25,000 tons, which turns out to be about 43 ms. You'll have to extract all of this

263
01:03:16.590 --> 01:03:21.509
WH11NE- Sunrise: circulating it, which is extremely challenging. And, in fact, this is the

264
01:03:21.690 --> 01:03:36.369
WH11NE- Sunrise: this is the fastest spill time in the history of dream physic that I know of. At least so people do slow extraction in medical machines whereby we want to get a radiation treatment. They do this slow spill, but that's typically over

265
01:03:36.530 --> 01:03:51.279
WH11NE- Sunrise: 15 seconds or something like that. But here we have a spill time of about 43 ms, which is ridiculously fast. So all the hardware and everything has to be on point. And it's challenging. And that's also why it's it's exciting. So so yeah, spill time is extremely strong.

266
01:03:52.420 --> 01:04:10.579
WH11NE- Sunrise: very thesis. I did not want to use the word slow, but people won't understand. So yeah, yeah, on beam monitor. You mentioned the wall current monitors? Yeah. So how? What is the effect of that on the beam itself, on the beam back? So

267
01:04:10.660 --> 01:04:27.264
WH11NE- Sunrise: that's a good question. So this thing, this thing called impedance matching. So typically, we choose the material and the setup such that it actually will not have any. There won't be any fields penetrating the beam pipe, and to give the effect back to the beam. But

268
01:04:27.800 --> 01:04:56.549
WH11NE- Sunrise: there are other effects caused by beam pipe, such as space charge effects and which I'm not talking about. But in these diagnostics, typically you try to keep it as possible. Yeah, to the extent that, in fact, it's okay. And then I mean, so that was in the longitudinal for the transverse. Do you have anything right now to? Yeah. So in fact, the beam position monitor that I talked about was, in fact, a transverse measurement where it measures the transverse position of the beams. Centroid.

269
01:04:56.710 --> 01:05:00.922
WH11NE- Sunrise: So, yeah, so so if you see here,

270
01:05:01.760 --> 01:05:26.069
WH11NE- Sunrise: this is for transfers. This is transfers. Yes, so in fact, you would have. You could have in the horizontal direction. But you could also have plates in the, in the vertical direction you can figure out whether beam is in X or y. Is this what you use to actually measure the the yes, exactly. So. This beautiful triangle that I got was measured during Ppms in 2 locations.

271
01:05:28.580 --> 01:05:36.509
WH11NE- Sunrise: Okay, if we don't have more question, I think we can thank our speaker again.

272
01:05:38.460 --> 01:05:41.280
WH11NE- Sunrise: Stop sharing up next week.