Abstract
The electric field potential of an intense axially symmetric electron beam with parameters typical of electron cooling systems in proton (ion) synchrotrons is calculated. A general case of electrons of relativistic energy is considered.
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Notes
Equation (8) is also valid for the values of total energy of the electron and ion, as well as for the value of the ion energy per nucleon. In the latter case, mi is the mass of the nucleon in the ion nucleus.
For numerical calculations, it is convenient to calculate the beam current \({{I}_{e}}\) in amperes and the potentials in kilovolts, for which we can use the constants \(m{{c}^{3}}{\text{/}}e\) = 17033 A and \(m{{c}^{2}}{\text{/}}e\) = 511.0034 kV. Then we obtain the constant \({{C}_{\varphi }}\) = \(\frac{{2e{{I}_{e}}}}{{{{m}_{e}}{{c}^{3}}}}\) · \(\frac{{{{m}_{e}}{{c}^{2}}}}{{e{{\varphi }_{0}}}}\) · \(\frac{1}{{r_{b}^{2}}}\mathop \smallint \nolimits_0^{{{r}_{b}}} \frac{{r \cdot dr}}{{~~{{\beta }_{e}}\left( r \right)}}\).
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Translated by M. Samokhina
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Maltseva, J.L., Melnikov, S.A., Meshkov, I.N. et al. Space Charge of an Electron Beam in an Electron Cooling System. Phys. Atom. Nuclei 86, 2439–2445 (2023). https://doi.org/10.1134/S1063778823110285
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DOI: https://doi.org/10.1134/S1063778823110285