• R.C. Davidson, M. Dorf, I. Kaganovich, H. Qin, E. Startsev
  PPPL, Princeton, New Jersey

Funding: Research supported by the U. S. Department of Energy.

This paper presents a survey of the present theoretical understanding based on advanced analytical and numerical studies of collective interactions and instabilities for intense one-component ion beams, and for intense ion beams propagating through background plasma. The topics include: discussion of the condition for quiescent beam propagation over long distances; the electrostatic Harris instability and the transverse electromagnetic Weibel instability in highly anisotropic, one-component ion beams; and the dipole-mode, electron-ion two-stream instability (electron cloud instability) driven by an unwanted component of background electrons. For an intense ion beam propagating through a charge-neutralizing background plasma, the topics include: the electrostatic electron-ion two-stream instability; the multispecies electromagnetic Weibel instability; and the effects of a velocity tilt on reducing two-stream instability growth rates. Operating regimes are identified where the possible deleterious effects of collective processes on beam quality are minimized.

• M. Dorf, R.C. Davidson, H. Qin, E. Startsev
  PPPL, Princeton, New Jersey

Funding: Research supported by the U.S. Department of Energy.

This paper reports on recent advances in the development of a numerical scheme for describing the quiescent loading of a quasi-equilibrium beam distribution matched to a periodic focusing lattice*. The scheme allows for matched-beam distribution formation by means of the adiabatic turn-on of the oscillating focusing field, and it is examined here for the cases of alternating-gradient quadrupole and periodic solenoidal lattices. Furthermore, various distributions are considered for the initial beam equilibrium. The self-similar evolution of the matched-beam density profile is observed for arbitrary choice of initial distribution function and lattice type. The numerical simulations are performed using the WARP particle-in-cell code.

* M.Dorf et al., Phys. Rev. ST Accel. Beams, submitted for publication(2009).

• H. Qin, R.C. Davidson
  PPPL, Princeton, New Jersey

Funding: Supported by the U.S. Department of Energy.

Courant-Snyder (CS) theory is generalized to the case of coupled transverse dynamics with two degree of freedom. The generalized theory has the same structure as the original CS theory for one degree of freedom. The four basic components of the original CS theory, i.e., the envelope equation, phase advance, transfer matrix, and the CS invariant, all have their counterparts, with remarkably similar formal expressions, in the generalized theory presented here. The unique feature of the generalized CS theory is the non-commutative nature of the theory. In the generalized theory, the envelope function is generalized into an envelope matrix, and the envelope equation becomes a matrix envelope equation with matrix operations that are not commutative. The generalized theory gives a new parameterization of the 4D symplectic transfer matrix that has the same structure as the parameterization of the 2D symplectic transfer matrix in the original CS theory.

• H. Qin, R.C. Davidson
  PPPL, Princeton, New Jersey

Funding: Supported by the U.S. Department of Energy.

For applications of high-intensity beams in heavy ion inertial confinement fusion and high energy density physics, solenoidal focusing lattice and transverse wobblers can be used to achieve uniform illumination of the target and for suppressing deleterious instabilities. A generalized self-consistent Kapchinskij-Vladimirskij solution of the nonlinear Vlasov-Maxwell equations is derived for high-intensity beams in a solenoidal focusing lattice with transverse wobblers. The cross-section of the beam is an ellipse with dynamical centroid, titling angle, and transverse dimensions that are determined from 5 envelope-like equations.