Warm-fluid equilibrium theory of a thermal charged-particle beam in a periodic solenoidal focusing field

Abstract

A warm-fluid equilibrium theory is presented which describes a new thermal equilibrium of a rotating charged-particle beam in a periodic solenoidal focusing field. Warm-fluid equations are solved in the paraxial approximation. The rms beam envelope, the density and flow velocity profiles, and the self-consistent Poisson equations are derived. Density profiles are calculated numerically for high-intensity and low-intensity beams. Temperature effects in such beams are investigated. Radial confinement of the beam is discussed.

Simulation of periodically focused, adiabatic thermal beams

“…Furthermore, if one attempts to describe a realistic beam using the concept of an equivalent KV beam [1], the quadratic temperature profile induces an artificially repulsive pressure force, resulting in not only a unrealistically lower density of the beam on the axis but also unrealistic beam dynamics in phase space [15]. In this paper, we report results of two-dimensional (2D) particle-in-cell (PIC) simulations which further validate the theoretical predictions of the adiabatic thermal beam equilibrium [11][12][13]. In particular, we discuss simulation results for adiabatic thermal beams that do not rotate in the Larmor frame.…”

“…Recently, adiabatic thermal beam equilibrium has been predicated theoretically in a periodic solenoidal magnetic focusing field [11][12][13]. In general, an adiabatic thermal equilibrium corresponds to a spatially-varying equilibrium state in the zero-order approximation of the Boltzmann equation.…”

“…In particular, the existence of the adiabatic thermal beam equilibrium was shown in the framework of kinetic theory and equivalent warm-fluid theory. In the warm-fluid theory of the adiabatic thermal beam equilibrium [11,12], warm-fluid equations were solved in the paraxial approximation. The equation of state was adiabatic.…”

Dynamics of charged particles in an adiabatic thermal beam equilibrium

“…For example, the KV equilibrium model cannot be used to explain the beam tails in the radial distributions observed in recent high-intensity beam experiments [5]. Recently, adiabatic thermal beam equilibria have been discovered in a periodic solenoidal magnetic focusing field [6][7][8] and an AG quadrupole magnetic focusing field [8,9]. The measured density distribution [5] matches that of the adiabatic thermal beam equilibrium in a spatially varying solenoidal magnetic focusing field [6,8].…”

Simulation of adiabatic thermal beams in a periodic solenoidal magnetic focusing field

“…Recently, the adiabatic thermal beam equilibrium has been predicted theoretically in a periodic solenoidal magnetic focusing field [11][12][13]. In general, an adiabatic thermal equilibrium corresponds to a spatially varying equilibrium state in the zero-order approximation of the Boltzmann equation.…”