Scaling of the plasma sheath in a magnetic field parallel to the wall

Motivated by the magnetized target fusion [R. E. Siemon et al., Comments Plasma Phys. Controlled Fusion 18, 363 (1999)] experiment, a systematic investigation of the scaling of a one-dimensional plasma sheath with a magnetic field parallel to the wall was carried out using analytical theory and the particle-in-cell code VPIC [K. J. Bowers et al., Phys. Plasmas 15, 055703 (2008)]. Starting with a uniform Maxwellian distribution in three-dimensional velocity space, plasma consisting of collisionless electrons, and ions of the same temperature interacts with a perfectly absorbing wall. A much larger ion Larmor radius causes the wall to be charged positively, creating an electric field that tends to repel the ions and attract the electrons, which is the opposite of the conventional Bohm sheath [D. Bohm, Characteristics of Electrical Discharges in Magnetic Fields (McGraw-Hill, New York, 1949)]. This manifests in the form of gyro-orbit modification by this spatially varying electric field, the degree of which is found to intricately depend on the relation between three parameters: electron and ion thermal Larmor radii and plasma Debye length: ρthe, ρthi, and λD. Furthermore, the study of the sheath width scaling through the analysis of the full width at half max of electric field, xEh, elucidates three distinct types of behavior of xEh, corresponding to three different regimes: ρthi<λD, ρthe<λD<ρthi, and λD<ρthe. In addition to the sheath width, the scaling of the wall potential φWall, as well as the role of the ion mass and charge Z are investigated. The results of this analytical and computational approach can also be useful in studying the plasma sheath in the conventional magnetic confinement devices, in particular at the first wall of tokamaks.