% Tutorial 3
% Neutron Star

% load constants (in SI units)
set_constants

% The proton with an energy of 10 TeV is ultra-relativistic. We can thus calculate its momentum by dividing the energy by the speed of light:

E = 10e12 * e;
p = E/c
B = 1e8

% The radius of the particle trajectory is:

rho = p/(e*B)

% The circumference is:

circ = 2*pi * rho

% As the particle moves (almost) with the speed of light, the revolution frequency is:

f = c/circ

% The particle is ultra-relativistic. It emits synchrotron radiation.

gamma = E / (m_p * c^2)

% The total synchrotron radiation power is:

P = e^2*c / (6*pi * epsilon_0) * gamma^4 / rho^2

% Energy lost per turn:

U_0 = e^2 * gamma^4 / (3*epsilon_0 * rho)

% in eV:

U_0 / e

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