% Swiss Light Source
% This worksheet will use SI units; of course, the same results can be obtained with eV units.

% load some common constants:
set_constants
% circumference
circ = 290.4;
% particle energy
E_0 = 2.4e9 * e;
% damping partitions
j_x = 1.71; j_y = 1; j_z = 1.29;
% synchrotron radiation integrals
I_2 = 1.186; I_4 = -0.842;
% synchrotron radiation constant
C_gamma = e^2 / (3 * epsilon_0 * (m_e * c^2)^4)

% (This is the same as the 8.846e-5 m/GeV^3 quoted in the lecture on Slide 38)

C_gamma_from_lecture = 8.846e-5 / (1e9 * e)^3

% Calculate the time it takes particles to go around the ring once, and the energy loss per turn:

T_0 = circ / c
U_0 = C_gamma / (2*pi) * E_0^4 * I_2
% or, in eV:
U_0/e

% Now, we are ready to calculate the radiation damping times:

tau_x = 2/j_x * E_0/U_0 * T_0
tau_y = 2/j_y * E_0/U_0 * T_0
tau_z = 2/j_z * E_0/U_0 * T_0

% Large Hadron Collider

% circumference
circ = 27e3;
% particle energy
E_0 = 7e12 * e;
%revolution time
T_0 = circ / c

% For the synchrotron radiation constant, we now have to use the proton mass instead of the electron mass!

% synchrotron radiation constant
C_gamma = e^2 / (3 * epsilon_0 * (m_p * c^2)^4)

% Note that this is thirteen orders of magnitude smaller, because the mass is a factor 2000 smaller!

% quick check
2000.0^4

% Next, we will need to compute the second synchrotron radiation integral. We assume that synchrotron radiation is only emitted in the arcs.

rho = 2900;
total_arc_length = 2*pi * rho

% Since the radius of curvature is constant in the arcs, and we assume no further dipole magnets or wigglers, the value of the integrand in the second synchrotron radiation integral is constant (in the arcs), or zero (in the straights): I_2 = int (1/rho^2) ds = total_arc_legnth / rho^2

I_2 = total_arc_length / rho^2

% Now we are ready to calculate the energy loss per turn

U_0 = C_gamma / (2*pi) * E_0^4 * I_2
% in eV:
U_0/e

% Calculate the Lorentz factor gamma:

gamma = E_0 / (m_p * c^2)

% The critical photon energy is:

epsilon_c = 3/2 * hbar*c/rho * gamma^3
% in eV:
epsilon_c/e

% (This is deep UV radiation.)
% Now we can calculate the damping time (we know that the vertical partition number j_y is always 1):

tau_y = 2/j_y * E_0/U_0 * T_0
% in days:
tau_y / (24*60*60)

% Now, for LEP:

% particle energy
E_0 = 100e9 * e;
% synchrotron radiation constant
C_gamma = e^2 / (3 * epsilon_0 * (m_e * c^2)^4)
U_0 = C_gamma / (2*pi) * E_0^4 * I_2
% in eV:
U_0/e

% Indeed, the synchrotron radiation losses in LEP were larger than they are in LHC now…

gamma = E_0 / (m_e * c^2)

% Critical photon energy:

epsilon_c = 3/2 * hbar*c/rho * gamma^3
% in eV:
epsilon_c/e

% …and the photons had a much higher critical energy in LEP!
% The vertical damping time is:

tau_y = 2/j_y * E_0/U_0 * T_0

%