A Paul trap configuration to simulate intense non-neutral beam propagation over large distances through a periodic focusing quadrupole magnetic field
A Paul trap configuration to simulate intense non-neutral beam propagation over large distances through a periodic focusing quadrupole magnetic field
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保罗陷阱配置，用于模拟通过周期性聚焦四极磁场长距离的强非中性光束传播
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发表时间：
2000
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通讯作者：
G. Shvets
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作者：
R. Davidson;H. Qin;G. Shvets
本文研究了强流非中性带电粒子束在周期聚焦四极磁场中沿z方向的传输，该磁场对粒子具有横向聚焦力−κq（s）[xex−yey]。这里，s=βbct是轴向坐标，（γB−1）mbc 2是束粒子的定向轴向动能，q B和mb分别是束粒子的电荷和静止质量，振荡晶格系数满足κq（s+S）=κq（s），其中S是聚焦场的轴向周期长度。假设粒子在束系中的运动是非相对论性的，用Vlasov-Maxwell方程描述特征半径为rb <$S的细束在横向实验室系相空间（x，y，x′，y′）中分布函数fb（x，y，x′，y′，s）和（归一化）自场势<$b（x，y，s）=qbφ（x，y，s）/γ b3 mb β b2 c2的非线性演化.研究表明，集体过程和非线性横向束动力学可以在紧凑的保罗陷阱配置中模拟，其中长的非中性等离子体柱（L rp）通过在z=±L处的端柱上施加直流电压V=const而轴向限制，并且x-y平面中的横向限制由分段圆柱形电极（半径rw）提供，并在90°段内施加振荡电压±V0（t）。这里，V0（t+T）=V0（t），其中T=const是振荡周期，作用在圆柱轴附近的电荷为q、质量为m的粒子上的振荡四极聚焦力为−mκq（t）[xex−yey]，其中κq（t）<$8qV0（t）/π mrw 2.本文研究了强流非中性带电粒子束在具有横向聚焦力的周期聚焦四极磁场中沿z方向的传输，−κq（s）[xex−yey]，在束粒子上。这里，s=βbct是轴向坐标，（γB−1）mbc 2是束粒子的定向轴向动能，q B和mb分别是束粒子的电荷和静止质量，振荡晶格系数满足κq（s+S）=κq（s），其中S是聚焦场的轴向周期长度。假设粒子在束系中的运动是非相对论性的，用Vlasov-Maxwell方程描述特征半径为rb <$S的细束在横向实验室系相空间（x，y，x′，y′）中分布函数fb（x，y，x′，y′，s）和（归一化）自场势<$b（x，y，s）=qbφ（x，y，s）/γ b3 mb β b2 c2的非线性演化.结果表明，集体过程和非线性横向束流动力学可以模拟。
This paper considers an intense non-neutral charged particle beam propagating in the z-direction through a periodic focusing quadrupole magnetic field with transverse focusing force, −κq(s)[xex−yey], on the beam particles. Here, s=βbct is the axial coordinate, (γb−1)mbc2 is the directed axial kinetic energy of the beam particles, qb and mb are the charge and rest mass, respectively, of a beam particle, and the oscillatory lattice coefficient satisfies κq(s+S)=κq(s), where S is the axial periodicity length of the focusing field. The particle motion in the beam frame is assumed to be nonrelativistic, and the Vlasov-Maxwell equations are employed to describe the nonlinear evolution of the distribution function fb(x,y,x′,y′,s) and the (normalized) self-field potential ψ(x,y,s)=qbφ(x,y,s)/γb3mbβb2c2 in the transverse laboratory-frame phase space (x,y,x′,y′), assuming a thin beam with characteristic radius rb≪S. It is shown that collective processes and the nonlinear transverse beam dynamics can be simulated in a compact Paul trap configuration in which a long non-neutral plasma column (L≫rp) is confined axially by applied dc voltages V=const on end cylinders at z=±L, and transverse confinement in the x−y plane is provided by segmented cylindrical electrodes (at radius rw) with applied oscillatory voltages ±V0(t) over 90° segments. Here, V0(t+T)=V0(t), where T=const is the oscillation period, and the oscillatory quadrupole focusing force on a particle with charge q and mass m near the cylinder axis is −mκq(t)[xex−yey], where κq(t)≡8qV0(t)/πmrw2.This paper considers an intense non-neutral charged particle beam propagating in the z-direction through a periodic focusing quadrupole magnetic field with transverse focusing force, −κq(s)[xex−yey], on the beam particles. Here, s=βbct is the axial coordinate, (γb−1)mbc2 is the directed axial kinetic energy of the beam particles, qb and mb are the charge and rest mass, respectively, of a beam particle, and the oscillatory lattice coefficient satisfies κq(s+S)=κq(s), where S is the axial periodicity length of the focusing field. The particle motion in the beam frame is assumed to be nonrelativistic, and the Vlasov-Maxwell equations are employed to describe the nonlinear evolution of the distribution function fb(x,y,x′,y′,s) and the (normalized) self-field potential ψ(x,y,s)=qbφ(x,y,s)/γb3mbβb2c2 in the transverse laboratory-frame phase space (x,y,x′,y′), assuming a thin beam with characteristic radius rb≪S. It is shown that collective processes and the nonlinear transverse beam dynamics can be simulated ...