Q&A SC Workshop 05.11.19 (Tuesday afternoon session)
reported by Malte Titze

Q: Question
A: Answer
C: Comment from someone in the audience


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"On the boundary between coherent and incoherent effects"
Giuliano Franchetti

Q: Did you ever computed the self-consistent potential of an individual particle? Is there a separatrix? Is the beam
trapped in the separatrix collectively?
A: Going to -0.90 example: For this tune depression you can forget about doing a 'normal' simulation. 
In principle this question is open. But in this case here, if I add a modulated gradient, I got basically the same results as Sacherer (regarding envelope motion).

Q: The transition incoherent/collective "I<1 or I>3" in order to characterize collective/non-collective effects looks a bit arbitrary. It seems to be more like a smooth transition. 
A: What is nice is that we have such a characterization at all. But of course it will be a matter of definition what you call more collective or non-collective. Regarding 3 I chose this value because in the case of a Gaussian distribution 3 is basically the edge of the distribution.
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"Space-charge particle resonances and mode parametric resonances"
Dong-O Jeon

Q: Regarding the envelope instability on the 4th order: Ingo made simulations in the experiment of GSI in which the envelope mode would take over if the LINAC would be longer.
A: Only if you keep the lattice $\sigma_0$ a constant. But if you keep the lattice $\sigma$ constant, you won't see it.

Q: On slide 13 (4th order instability): For that working point you showed there: Did you calculate the envelope instability stopband width and is that working point inside or outside of the stopband? I believe the envelope instability is still there, even though the tails of a 4th order resonance are visible. Could you perhaps go to the case similar to what Ingo showed yesterday (2nd order envelope instability)?
A: Going to slide 11: I think its still inside the stopband.
Q: Then I would call it envelope instability. (Still on slide 11) It seems that the resonance is already there, right from the beginning.
A: The 4th order resonance appears first, it is however difficult to explain at this point.

C: If one amplitude is growing linearly and one is exponentially, then you might see one at the beginning just one and the other at a later time. If you would start mismatched, you would expect only the envelope oscillations. But since you start very well matched, you might first see the incoherent one.
A: Yes, if initially there would be a mismatch, I guess the envelope instability will be seen first. 
C: Indeed the time evolution might be different.

Q/C: But in your simulations you can not be perfectly matched, there is always a small mismatch. This should be investigated further.

A: At the GSI UNILAC experiment where we matched in "rms sense" the beam from injector to the ETR (?) and then we observed the 4th order resonance. 

Q: Why don't you see any mode excited in the FFT spectrum?
C: If one takes an FFT of the moments, you might see a signal.
C: Ok this should be done perhaps in this case.

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"Comments on the coherent and incoherent views"
Shinji Machida

C/Q: I did similar simulations for the dependency on Q_s. We saw the increases you described but then it goes down again to the 2D case, because the synchrotron frequency is too slow and you get very little emittance growth. We need to ensure that the increase in the synchrotron frequency is at the right magnitude to avoid entering a coasting beam scenario.
A: Indeed, I attempted to do this in the simulation in order to avoid this.
C: We are operating at around 5% losses, so we need to be very careful how we are looking at this.
A: The idea is to make the frequency smaller, so we expect more beam loss.

Q: Is there a machine worldwide that seems to be affected by coherent resonances that we are not aware off?
A: Certainly we can make a coherent resonance artificial but usually that is not how it is done in operation.

Q: Regarding your proposed experiment: We should be able to do that, but what intensity do you need in the PS (to be increased by 63%)?
A: Whatever you can do seems to be fine.
C: Seems to be possible.

Q: Can you give a clear definition of what you understand by coherent resonance?
A: The coherent resonance is defined as a resonance of the beam envelope.

Q: But Ingo considered higher order modes ...
A: Yes if you want to go to higher order you need the Vlasov model.

C: What Ingo had on his slides is the externally driven coherent linear resonance. But we are talking here only about the parametric internally driven resonance (which is exponential) and the single-particle incoherent resonance. But the external coherent resonances exists for any order, but might be very weak because you drive it from outside.
A: I don't think there is any externally coherent driven resonance in my talk.

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"Progress toward testing non-linear integrable optics in a Paul trap"
Lucy Martin

Q: You relied on transverse MCP but they usually had saturation issues: Did you managed to overcome this?
A: We will operate in a region where we do not saturate the MCP. Also we have discovered that you can correct such saturation with
enough power supplies (which we don't have).

Q: Do you have experiments planned once you had the octupole up and running -- and may I suggest an experiment?
A: Sure. We ourselves were thinking about excite a resonance inside a tunespread and look at the number of ions which we can extract with and without different octupole voltages.
Q/C: My suggestion would be to investigate how one can match into these optics channels? Because our simulations with a KV beam showed that everything just sprayed off to infinity -- and we had to use a matched beam. One way one can do this might be to adiabatically ramp the octupole strength.
A: Good idea and let us know any other ideas.

C/Q: I don't think you have an analogue to a coasting beam. I believe that you have an analogue to a square barrier bucket.
A: Our longitudinal motion is very slow, so it is a barrier kick but an almost infinite long one, so it would be like a coasting beam.

Q: Are you planning any bunch-analysis in your project which is not related to losses?
A: Yes, one of the disadvantages of the Paul trap is the diagnostics. In Japan we performed an experiment using a dipole kick and were able to measure the beta-function. Also we would like to install a fast camera at the time when we extract, which can serve as a time-slice for the beta-function. However such a device is rather expensive and the statistics are not optimal.

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"Effects of detuning impedance, chromaticity, transverse damper, linear
coupling, Landau damping and space charge on TMCI"
Elias Métral

C: SC shifts the coherent head-tail-modes, but SC can also cause Landau damping.
A: That's why I put all of these things together, hoping that we might understand better:
If you have some modes coupling inside the tunespread, you can generate instabilities.
The intensity threshold from mode-coupling is reduced by Landau damping, as it was first studied in 1985 by Yong Ho Chin (https://cds.cern.ch/record/160217/files/198507010.pdf). This was also recovered in my own analytical studies. To be finalised and in particular confirmed by macro particle tracking simulations.
Furthermore, Nicolas Mounet started some pyHEADTAIL studies and saw a lower threshold as predicted, but the study has to be finalised.

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"Beam profile measurements based on pixel detectors in the PS"
Hampus Sandberg

Q: What about the jet-profile. Is it injected?
A: The profiles are gas-injected ... (acoustic bad!)
Q: Can you use machine learning to help expand the range of the IPM's?
A: Yes we have some colleagues from GSI which took the old IPM data from the LHC where we had this problem with SC, because the old magnet was not strong enough, leading to a deformed profile. So they simulated the bunch how they expect it to be, then feed it into the machine learning model to convert it back to the actual profile.
Q: Could you comment on the simulation (parameters) on Slide 4? 
A: Yes, the flat-top belongs to the case after the beam was accelerated. And the other ones are at injection.
A/C: So the intensities are pretty much the same. The idea was to show that the concept works for the LHC so that we can implement it.

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"Space charge issues in FFAs"
Jean-Baptiste Lagrange

C/Q: There was a paper by Etienne 1998 related to linear coupling. Do you have coasting or bunched beam?
A: bunched.
C/Q: There are several ways to define a beta-function. But they have usually no physical meaning. How can we make a connection between the beta-function and the beam size in such coupled scenarios?
C: Ripken has the idea of two vectors, one for each beta-function (further discussion about beta-functions in the audience).
C: There is a scaling factor from your invariance, which is your beta-function.
Q: Can we calculate the tune-shift from SC as a function of ... the beta-function perhaps? or the emittance? In a decoupled space?
That would give you the physical meaning.
C: One can use Ripken/Willeke notion of beta-function as a start.
Q: If you go around the machine, is there are torsion component?
A: Overall it has to be periodic.
Q: What is the shape of the beam in this vertical FFAG: Is it tall, narrow or long?
A: Going to slide 14: This is the phase space in horizontal and vertical, respectively.