Kinetic description of electron-proton instability in high-intensity proton linacs and storage rings based on the Vlasov-Maxwell equations

Abstract

The present analysis makes use of the Vlasov-Maxwell equations to develop a fully kinetic description of the electrostatic, electron-ion two-stream instability driven by the directed axial motion of a highintensity ion beam propagating in the z direction with average axial momentum g 21͞2 . Furthermore, the ion motion in the beam frame is assumed to be nonrelativistic, and the electron motion in the laboratory frame is assumed to be nonrelativistic. The ion charge and number density are denoted by 1Z b e and n b , and the electron charge and number density by 2e and n e . For Z b n b . n e , the electrons are electrostatically confined in the transverse direction by the space-charge potential f produced by the excess ion charge. The equilibrium and stability analysis retains the effects of finite radial geometry transverse to the beam propagation direction, including the presence of a perfectly conducting cylindrical wall located at radius r r w . In addition, the analysis assumes perturbations with long axial wavelength, k bb and increasing fractional charge neutralization f. In addition, the instability is strongest (largest growth rate) for perturbations with azimuthal mode number ᐉ 1, corresponding to a simple (dipole) transverse displacement of the beam ions and the background electrons. For the case of overlapping step-function density profiles for the beam ions and background electrons, corresponding to monoenergetic ions and electrons, a key result is that there is no threshold in beam intensityv 2 pb ͞v 0 2 bb or fractional charge neutralization f for the onset of instability. Finally, for the case of continuously varying density profiles with parabolic profile shape, a semiquantitative estimate is made of the effects of the corresponding spread in (depressed) betatron frequency on stability behavior, including an estimate of the instability threshold for the case of weak density nonuniformity. [S1098-4402(99) 00035-X]

Three-dimensional multispecies nonlinear perturbative particle simulations of collective processes in intense particle beams

“…We consider a thin, continuous, highintensity ion beam ͑ j b͒, with characteristic radius r b propagating in the z direction through background electron and ion components ͑ j e, i͒, each of which is described by a distribution function f j ͑x, p, t͒ [10][11][12]. The charge components ͑ j b, e, i͒ propagate in the z direction with characteristic axial momentum g j m j b j c, where V j b j c is the average directed axial velocity, g j ͑1 2 b 2 j ͒ 21͞2 is the relativistic mass factor, e j and m j are the charge and rest mass, respectively, of a jth species particle, and c is the speed of light in vacuo.…”

“…For example, a background population of electrons can result by secondary emission when energetic beam ions strike the chamber wall, or through ionization of background neutral gas by the beam ions. When a second charge component is present, it has been recognized for many years, both in theoretical studies and in experimental observations [12][13][14][15][16][17][18][19][20][21], that the relative streaming motion of the high-intensity beam particles through the background charge species provides the free energy to drive the classical two-stream instability [22], appropriately modified to include the effects of dc space charge, relativistic kinematics, presence of a conducting wall, etc. A well-documented example is the electron-proton (e-p) instability observed in the Proton Storage Ring (PSR) [17,18], although a similar instability also exists for other ion species including (for example) electron-ion interactions in electron storage rings [19 -21].…”

“…The present paper reports recent advances in applying the df formalism to investigate nonlinear collective processes in intense charged particle beams. The BEST ( beam equilibrium, stability, and transport) code [25] described here is a newly developed 3D multispecies nonlinear perturbative particle simulation code, which can be applied to a wide range of important collective processes in intense beams, such as the electron-ion two-stream instability [12][13][14][15][16][17][18] and the periodically focused beam propagation [11]. While several features of the 3D BEST code are summarized in Ref.…”

Overview of theory and modeling in the heavy ion fusion virtual national laboratory

“…Assisted-pinched transport uses a preformed 50-kA channel, created in a gas (1)(2)(3)(4)(5)(6)(7)(8)(9)(10) by a laser and a discharge electrical circuit, to create a frozen magnetic field before the heavy ion beam is injected [43][44][45]. Self-pinched transport uses the ion beam itself to break down a low-pressure gas (1-100 mTorr) [13,46,47], and the net self-magnetic field affords confinement.…”

“…Examples include: detailed analytical and nonlinear perturbative simulation studies of collective processes, including the electron-ion two-stream instability [2][3][4][5][6][7], and the Harrislike temperature-anisotropy instability driven by T ⊥b T b [8][9][10][11]; development of a selfconsistent theoretical model of charge and current neutralization for intense beam propagation through background plasma in the target chamber [12][13][14][15]; development of a robust theoretical model of beam compression dynamics and nonlinear beam dynamics in the final focus system using a warm-fluid description [16]; development of an improved kinetic description of nonlinear beam dynamics using the Vlasov-Maxwell equations [2,[17][18][19][20], including identification of the class of (stable) beam distributions, and the development of…”