The secondary electron emission coefficient is evaluated for electron impact on anode, cathode, and electrically floating plasma-facing surfaces. Two energy and angle distribution functions for electron impact on a plasma-facing surface are derived and different relations for the secondary electron emission coefficient which functionally depend on energy and angle are integrated over the distributions. One integration is in closed form and provides a parametric expression for the secondary electron emission coefficient of a plasma-facing surface. The other integrations are carried out numerically. Evaluation of the secondary electron emission coefficient for a variety of commonly-used plasma-facing materials shows that its value is near or above unity over a significant range of plasma temperatures.
The fully kinetic, one-dimensional, plasma-sheath theory by Schwager and Birdsall [Phys. Fluids B 2, 1057 (1990)] is further developed. A cold-electron emitting surface is included and a three-dimensional plasma is considered. The sheath potential is not assumed to equal the floating potential so that the theory applies to a current-carrying sheath. Appropriate values are found for higher-order moments of the velocity distribution which depend on the three-dimensional velocity distribution width. Distribution functions in terms of energy and angle are derived. The (effective) temperature, the total energy flux, and the heat flux are evaluated in terms of exact analytic functions. The normalized magnitude of the floating potential for a deuterium plasma with equal ion and electron temperatures is calculated to be ψf=3.2 for δ=0 and ψf=1.8 for δ=0.75 where δ is the electron emission coefficient. The normalized magnitude of the sheath potential for the same plasma (with δ=0) is calculated to be ψs=3.9 for γ=0.02 and ψs=2.8 for γ=−0.02 where γ is the normalized current density. A self-consistent integral solution for the electrostatic potential profile within the sheath is derived.
The classical trajectory of an initially unbound positron within the electric field of an antiproton and a uniform magnetic field is simulated in three dimensions. Several simulations are run incorporating experimental parameters used for antihydrogen production, which has been achieved by two different groups [M. Amoretti, Nature (London) 419, 456 (2002); G. Gabrielse, Phys. Rev. Lett. 89, 213401 (2002)]. The simulations indicate that temporary bound states of antihydrogen can form at positive energies, where the energy of the system is defined to be zero when the positron and antiproton are at rest with infinite separation. Such quasibound states, which form only when the magnetic field is present, are typically smaller than in a dimension perpendicular to the magnetic field. An analytical model is developed for a formation cross section, and it is found that quasibound states may form more frequently than stable Rydberg states.
The Coulomb logarithm is a fundamental plasma parameter which is commonly derived within the framework of the binary collision approximation. The conventional formula for the Coulomb logarithm, λ=ln Λ, takes into account a pure Coulomb interaction potential for binary collisions and is not accurate at small values (λ<10). However, a more exact Fokker–Planck equation was recently presented by Li and Petrasso which is accurate at small Coulomb logarithm values (λ≳2) [Phys. Rev. Lett. 70, 3063 (1993)]. This theory and computer simulations which are accurate for small Coulomb logarithm values provide the motivation for a more precise evaluation of the Coulomb logarithm. In the present work, the Coulomb logarithm is evaluated more precisely by using a cutoff Coulomb interaction potential. The result is compared to an exact numerical evaluation of the Coulomb logarithm which considers a screened Coulomb interaction potential. Fits to the numerical results are also provided. The fitted formula λ=ln(0.6 Λ) is recommended for most applications providing values within 4% of the exact numerical values for λ≳2. This formula is easily implemented by using 0.6λD in place of λD (the Debye length) in the conventional formula for the Coulomb logarithm.
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