Calculate SURF III Accelerator Parameters

Uwe Arp1

Variable Parameters
Magnetic flux density 0.04 T ≤ B ≤ 1.7 T   T
RF frequency 113.8 MHz ≤ νRF ≤ 114.1 MHz   MHz
Magnetic field index 0 ≤ n ≤ 3/4
RF gap voltage -2 kV ≥ VRF ≥ -21 kV   kV
Electron beam current 0 mA ≤ IB ≤ 1000 mA   mA
Fixed & Derived Parameters
Orbital frequency $\nu_0 = \frac{\nu_{RF}}{h} $   MHz
Electron energy E0   MeV
Gamma factor $\gamma =\frac{E_0}{m_eC_I^2}$
Beta factor $\beta = \sqrt{ 1 - 1 / \gamma^2 }$
Orbital radius $\rho_0 = \frac{\beta \, C_I \, h}{2\pi \,\nu_{RF}}$   mm
Characteristic wavelength $\lambda_c = \frac{4\pi \, \rho_0}{3 \lambda^3}$   nm
Number of electrons $ N_e = \frac{I_B \, 2\pi\, \rho_0}{e_0 \, \beta \, c}$
Energy loss per turn $U_0 = \frac{e_0^2 \, \gamma^4}{3\varepsilon_0 \, \rho_0}$   eV
Radiated power per electron $P_\gamma = \frac{c_I \, e_0^2 \, \gamma^4}{6\pi \,\varepsilon_0 \, \rho_0}$   nW
Total radiated power $P_{\rm tot} - N_e \, P_\gamma$   W
Synchrotron Oscillation frequency $u_s = \nu_0 \sqrt{\frac{h e_0 V_{\rm RF}\cos(\psi_s)}{2\pi \beta E_0(n-1)}}$   kHz
Natural energy spread $\frac{\sigma_E}{E_0}=\sqrt{\frac{C_q \gamma^2}{\rho_0}\frac{1-n}{3-4n}}$   %