Generalized Kapchinskij-Vladimirskij Distribution and Beam Matrix for Phase-Space Manipulations of High-Intensity Beams.

In an uncoupled linear lattice system, the Kapchinskij-Vladimirskij (KV) distribution formulated on the basis of the single-particle Courant-Snyder invariants has served as a fundamental theoretical basis for the analyses of the equilibrium, stability, and transport properties of high-intensity beams for the past several decades. Recent applications of high-intensity beams, however, require beam phase-space manipulations by intentionally introducing strong coupling. In this Letter, we report the full generalization of the KV model by including all of the linear (both external and space-charge) coupling forces, beam energy variations, and arbitrary emittance partition, which all form essential elements for phase-space manipulations.

Field theory and weak Euler-Lagrange equation for classical particle-field systems.

It is commonly believed as a fundamental principle that energy-momentum conservation of a physical system is the result of space-time symmetry. However, for classical particle-field systems, e.g.

Generalized Courant-Snyder theory for charged-particle dynamics in general focusing lattices.

The Courant-Snyder (CS) theory for one degree of freedom is generalized to the case of coupled transverse dynamics in general linear focusing lattices with quadrupole, skew-quadrupole, dipole, and solenoidal components, as well as torsion of the fiducial orbit and variation of beam energy. The envelope function is generalized into an envelope matrix, and the phase advance is generalized into a 4D sympletic rotation. The envelope equation, the transfer matrix, and the CS invariant of the original CS theory all have their counterparts, with remarkably similar expressions, in the generalized theory.

Class of generalized Kapchinskij-Vladimirskij solutions and associated envelope equations for high-intensity charged-particle beams.

A class of generalized Kapchinskij-Vladimirskij solutions of the Vlasov-Maxwell equations and the associated envelope equations for high-intensity beams in an uncoupled lattice is derived. It includes the classical Kapchinskij-Vladimirskij solution as a special case. For a given lattice, the distribution functions and the envelope equations are specified by ten free parameters.

Centroid and envelope dynamics of high-intensity charged-particle beams in an external focusing lattice and oscillating wobbler.

The centroid and envelope dynamics of a high-intensity charged-particle beam are investigated as a beam smoothing technique to achieve uniform illumination over a suitably chosen region of the target for applications to ion-beam-driven high energy density physics and heavy ion fusion. The motion of the beam centroid projected onto the target follows a smooth pattern to achieve the desired illumination, for improved stability properties during the beam-target interaction. The centroid dynamics is controlled by an oscillating "wobbler," a set of electrically biased plates driven by rf voltage.

Generalized Kapchinskij-Vladimirskij distribution and envelope equation for high-intensity beams in a coupled transverse focusing lattice.

In an uncoupled lattice, the Kapchinskij-Vladimirskij (KV) distribution function first analyzed in 1959 is the only known exact solution of the nonlinear Vlasov-Maxwell equations for high-intensity beams including self-fields in a self-consistent manner. The KV solution is generalized here to high-intensity beams in a coupled transverse lattice using the recently developed generalized Courant-Snyder invariant for coupled transverse dynamics. This solution projects to a rotating, pulsating elliptical beam in transverse configuration space, determined by the generalized matrix envelope equation.

Enhanced self-focusing of an ion beam pulse propagating through a background plasma along a solenoidal magnetic field.

It is shown that the application of a weak solenoidal magnetic field along the direction of ion beam propagation through a neutralizing background plasma can significantly enhance the beam self-focusing for the case where the beam radius is small compared to the collisionless electron skin depth. The enhanced focusing is provided by a strong radial self-electric field that is generated due to a local polarization of the magnetized plasma background by the moving ion beam. A positive charge of the ion beam pulse becomes overcompensated by the plasma electrons, which results in the radial focusing of the beam ions.

Use of a linear Paul trap to study random noise-induced beam degradation in high-intensity accelerators.

A random noise-induced beam degradation that can affect intense beam transport over long propagation distances has been experimentally studied by making use of the transverse beam dynamics equivalence between an alternating-gradient (AG) focusing system and a linear Paul trap system. For the present studies, machine imperfections in the quadrupole focusing lattice are considered, which are emulated by adding small random noise on the voltage waveform of the quadrupole electrodes in the Paul trap. It is observed that externally driven noise continuously produces a nonthermal tail of trapped ions, and increases the transverse emittance almost linearly with the duration of the noise.

An exact magnetic-moment invariant of charged-particle gyromotion.

For the motion of a charged particle in a uniform, time-dependent axial magnetic field B(t)e(z), it is shown that there is an exact magnetic-moment invariant of the particle dynamics M, to which the adiabatic magnetic-moment invariant mu = mv2 perpendicular/2B is asymptotic when the time scale of the magnetic field variation is much slower than the gyroperiod. The connection between the exact invariant M and the adiabatic invariant mu enables us to characterize in detail the robustness of the adiabatic magnetic-moment invariant mu.

Paul trap simulator experiment to model intense-beam propagation in alternating-gradient transport systems.

The results presented here demonstrate that the Paul trap simulator experiment (PTSX) simulates the propagation of intense charged particle beams over distances of many kilometers through magnetic alternating-gradient (AG) transport systems by making use of the similarity between the transverse dynamics of particles in the two systems. Plasmas have been trapped that correspond to normalized intensity parameters s=omega(2)(p)(0)/2omega(2)(q) View Article and Find Full Text PDF