Investigation of the lifetime of a high-current beam in an ultraminiature storage ring

Use of a subminiature storage ring in a weak-current regime

“…In a subminiature storage ring [1,2], the orbit of the beam lies inside the cavity of the rf system, while in ordinary storage rings it passes through the rf cavity.The amplitude of the accelerating rf voltage U max and the energy acquired by an equilibrium particle over one revolution ΔE rev are related with one another by the well-known equation The weak-current regime considerably simplifies the construction of a magnetic system and decreases the likelihood of the development of bunch instabilities.…”

“…In a subminiature storage ring [1,2], the orbit of the beam lies inside the cavity of the rf system, while in ordinary storage rings it passes through the rf cavity. In a subminiature storage ring [1,2], the orbit of the beam lies inside the cavity of the rf system, while in ordinary storage rings it passes through the rf cavity.…”

“…The increment to the energy of an ultrarelativistic (γ >> 1, γ = (1 -β 2 ) -1/2 , β = υ/c, c~ 3·10 8 m/sec -light velocity) equilibrium particle over one revolution is Equation (2) was obtained by making the following substitutions in expression (1): cos (πx / d) ~ 1 -1/2(πx / d) 2 , x = R 0 cos (ϕ), cos (πz / a) = 1, ϕ = ω rf t. In addition, the derivation of Eq. The origin of the coordinates x, y, z lies at the center of the rectangular cavity.…”

“…The following empirical relation is proposed in [2] to obtain a more accurate estimate of the strength of the effect due to electron-electron scattering in a bunch: The following empirical relation is proposed in [2] to obtain a more accurate estimate of the strength of the effect due to electron-electron scattering in a bunch:…”

“…Table 1 shows that the new application of relation (5) [2] to some storage rings operating at reduced energy in a highcurrent regime. To find an approximate value of U max.thr the relation (4) must be equated to relation (5).…”