Resonances in Binary Charged-Particle Collisions in a Uniform Magnetic Field

Abstract

modulation n/n of approximately 5xl0~3 and a wavelength of 1.5 mm at the laser interaction volume located 135° around the torus from the wave guide. We scanned wavelength from 1 mm to 1 cm at positions of I from the center of the plasma to the limiter radius and did not observe the driven wave. The estimated sensitivity was greater than the expected level of fluctuations by a factor of 5.In the ATC, the thermal ion feature in the scattered spectrum is expected to be peaked near 400 MHz for a 1-mm-wavelength fluctuation. Scattering was not observed from this feature and this implies the absence of an ion-acoustic wave turbulence during the ATC discharge at levels larger than ten times the thermal level.We wish to acknowledge the collaboration of M. Porkolab in developing the C0 2 scattering diagnostic for plasma research, of J. Cecchi in interfacing the present apparatus to the ATC, and D. R. Moler in the design and operation of this experiment. We also are indebted to many members of the staff at the Princeton Plasma Physics Laboratory for helpful discussions and for their encouragement, and to the members of the ATC crew for their technical assistance. We also wish to acknowledge helpful conversations with to be published. 5 Hasegawa has called to our attention that at values of n/n of 10" 2 the nonlinear coupling of radial and poloidal modes through the E(k, a;) xB r drift of ions can produce an effective frequency shift comparable to the driftwave frequency LA. Hasegawa, Phys. Lett. 75A, 143 (1976)]. This might explain both the observed frequency spread at fixed wave vector and the isotropic nature of the turbulence in the plane perpendicular to B r .I have considered the two-body problem in a uniform magnetic field. For the case of like-particle collisions, a resonance between the velocities transverse to the magnetic field of the test and field particles reduces the problem to that without a magnetic field for the relative-velocity scattering angle and scattering cross section. This resonance condition results in large changes in the test-particle collisional parameters. A secondary resonance for like-particle and resonances for unlike-particle collisions have also been found.The binary collisional scattering and the related collisional parameters of a plasma in a magnetic field are important for the transport, 1 " 3 heating, 4 " 6 and magnetic confinement 7 * 8 of thermonuclear plasmas in open-ended as well as toroidal configurations. The transport of intense relativistie electron beams, radially confined by their self-pinch magnetic fields, through gas-plasma media over long distances, 9 as well as the interaction of intense electron beams with virtual cathodes in the presence of externally applied magnetic fields 10 also depend on the binary collisional scattering. Previous treatments 11 ' 12 of the binary collision problem in a magnetic field have been approximate, to the extent that ultimately only the maximum impact parameter is altered from the Debye length X D to an appropriate average Larmor radius...

Binary collisions of charged particles in a magnetic field

“…Numerical calculations have been performed for binary collisions (BC) between magnetized electrons [8,9] and for collisions between magnetized electrons and ions [10,11,12,13,14]. In general the total energy E of the particles interacting in a magnetic field is conserved but the relative and center of mass energies are not conserved separately.…”

Energy transfer in binary collisions of two gyrating charged particles in a magnetic field

“…In the presence of an external magnetic field, the Lagrangian and the corresponding equations of motion cannot be separated into parts describing the relative motion [r = r 1 − r 2 , v = ṙ] and the motion of the cm [R = (m 1 r 1 + m 2 r 2 )/(m 1 + m 2 ), V = Ṙ], in general. 7,11,[13][14][15][16] Introducing the reduced and the total masses 1/µ = 1/m 1 + 1/m 2 , M = m 1 + m 2 , respectively, and recalling that v ν (t) = V(t) + ̺ ν (µ/m ν )v(t) the equations of the relative and the cm motion are…”

“…Recent applications are the cooling of heavy ion beams by electrons [2][3][4][5] and the energy transfer for heavy-ion inertial confinement fusion. 6 Calculations have been performed for binary collisions (BC) between magnetized electrons 7,8 and for collisions between magnetized electrons and ions. [9][10][11][12][13][14][15][16] In the presence of a magnetic field only the total energy E of the interacting particles is conserved but not the relative and center of mass energies separately.…”

Interactions Between Charged Particles in a Magnetic Field

“…Numerical calculations have been performed for binary collisions (BC) between magnetized electrons [47,116] and for collisions between magnetized electrons and ions [135,136,138]. While the total energy W of the particles interacting in a magnetic field is a constant of motion, the relative and center of mass energies are not conserved separately.…”