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Generalized Courant–Snyder theory and Kapchinskij–Vladimirskij distribution for high-intensity beams in a coupled transverse foc

Generalized Courant–Snyder theory and Kapchinskij–Vladimirskij distribution for high-intensity beams in a coupled transverse focusing lattice

http://link.aip.org/link/doi/10.1063/1.3574919

Hong Qin1,2 and Ronald C. Davidson2

1Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543, USA  
2Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China

The Courant–Snyder (CS) theory and the Kapchinskij–Vladimirskij (KV) distribution for high-intensity beams in an uncoupled focusing lattice are generalized to the case of coupled transverse dynamics. The envelope function is generalized to an envelope matrix, and the envelope equation becomes a matrix envelope equation with matrix operations that are noncommutative. In an uncoupled lattice, the 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 to high-intensity beams in a coupled transverse lattice using the generalized CS invariant. This solution projects to a rotating, pulsating elliptical beam in transverse configuration space. The fully self-consistent solution reduces the nonlinear Vlasov-Maxwell equations to a nonlinear matrix ordinary differential equation for the envelope matrix, which determines the geometry of the pulsating and rotating beam ellipse. These results provide us with a new theoretical tool to investigate the dynamics of high-intensity beams in a coupled transverse lattice. A strongly coupled lattice, a so-called N-rolling lattice, is studied as an example. It is found that strong coupling does not deteriorate the beam quality. Instead, the coupling induces beam rotation and reduces beam pulsation.

Study of the change of electron temperature inside magnetic island caused by localized radio frequency heating

J. Yang, S. Zhu, Q. Yu, andG. Zhuang

Phys. Plasmas 17, 052309 (2010)

The change in the electron temperature inside magnetic island caused by localized radio frequency (rf) heating is studied numerically by solving the two-dimensional energy transport equation, to investigate the dependence of the temperature change on the location and width of the rf power deposition along the minor radius and the helical angle, the island width, and the ratio between the parallel and the perpendicular heat conductivity. Based on obtained numerical results, suggestions for optimizing the island stabilization by localized rf heating are made. 

Zonal flow modes in a tokamak plasma with dominantly poloidal mean flows

Deng Zhou( 周登 ),Phys. Plasmas 17, 102505 (2010)
The zonal flow eigenmodes in a tokamak plasma with dominantly poloidal mean flows are theoretically investigated. It is found that the frequencies of both the geodesic acoustic mode and the sound wave increase with respect to the poloidal Mach number. In contrast to the pure standing wave form in static plasmas, the density perturbations consist of a standing wave superimposed with a small amplitude traveling wave in the poloidally rotating plasma 

Charge shielding in magnetized plasmas

Shaojie Wang,Ulrich Stroth, and Guido Van Oost

Phys. Plasmas 17, 112101 (2010)

The shielding of a charge sheet in a magnetized plasma is investigated by taking account of the diamagnetic drift start-up current in addition to the polarization current. For a charge sheet with an infinitesimal width, the shielding is the same as the conventional Debye shielding if the charge sheet is perpendicular to the magnetic field; the shielding length is times larger than the conventional one if the charge sheet is parallel to the magnetic field. When the scale length of the charge sheet is comparable or smaller than the ion Larmor radius, the electric field is significantly enhanced within the charge sheet, while far away from the charge sheet, the electric field is shielded to the usual 1/εr level (where εr is the diamagnetic coefficient of the magnetized plasma).

Effect of impurity ions on the geodesic acoustic mode

Wenfeng Guo
Shaojie Wang, and 
Jiangang Li ,

Phys. Plasmas 17, 112510 (2010)

A dispersion relation of the geodesic acoustic mode with the effect of impurity ions is systematically derived. It is found that the frequency of the geodesic acoustic mode for a plasma with impurity ions is lower than that without impurity ions, which are mainly due to the polarization of impurity ions. It is also found that the damping rate of the mode increases with the increase in effective charge in the small effective charge limit due to the polarization currents of impurity ions, and decreases in the large effective charge limit mainly due to the effect of the curvature drift of impurity ions. A maximum damping rate is found in the intermediate effective charge regime.