A summary of closed-form expressions for the magnetic fields produced by rectangular- and circular-shaped finite-length solenoids and current loops is provided altogether for easy reference. Each expression provides the magnetic field in all space, except locations where a current of infinitesimal thickness is considered to exist. The closed-form expression for the magnetic field of a rectangular-shaped finite-length solenoid is derived using the Biot–Savart law. Closed-form expressions for the magnetic fields of solenoids and current loops can be used to avoid approximations in analytical models and may reduce computation time in computer simulations.
A Monte Carlo simulation is presented of an experiment that could potentially determine whether antihydrogen accelerates vertically up or down as a result of earth's gravity. The experiment would rely on methods developed by existing antihydrogen research collaborations and would employ a Penning trap for the production of antihydrogen within a uniform magnetic field. The axis of symmetry of the cylindrical trap wall would be oriented horizontally, and an axisymmetric aperture (with an inner radius that is smaller than the cylindrical trap wall radius) would be present a short distance away from the antihydrogen production region. Antihydrogen annihilations that occur along the cylindrical trap wall would be detected by the experiment. The distribution of annihilations along the wall would vary near the aperture, because some antihydrogen that would otherwise annihilate at the wall would instead annihilate on the aperture. That is, a shadow region forms behind the aperture, and the distribution of annihilations near the boundary of the shadow region is not azimuthally symmetric when the effect of gravity is significant. The Monte Carlo simulation is used together with analytical modeling to determine conditions under which the annihilation distribution would indicate the direction of the acceleration of antihydrogen due to gravity
A classical trajectory Monte Carlo simulation is used to investigate an artificially structured boundary for confinement and control of charged particles. The artificially structured boundary considered here incorporates a planar sequence of conducting wires, where adjacent wires carry current in opposite directions. Such a configuration creates a sequence of magnetic cusps and was studied previously [C. A. Ordonez, J. Appl. Phys. 106, 024905 (2009)]. The effect of introducing a sequence of electrodes for electrostatic plugging of the cusps is investigated. The results of the simulations are used to identify regions of parameter space in which particle losses through the cusps may be negligible in the single particle limit. A trap based on a cylindrical generalization of the artificially structured boundary presented here may lead to a method for confining non-neutral and partially neutralized plasmas along the edge, such that the bulk of a confined plasma is effectively free of externally applied electromagnetic fields.
A computer simulation is presented of single-species non-neutral plasma confinement using an artificially structured boundary. The artificially structured boundary produces a spatially periodic static electromagnetic field along the plasma periphery such that the spatial period of the applied field is much smaller than the dimensions of the confined plasma. The simulated non-neutral plasma self-consistently produces an electrostatic potential energy well for oppositely signed charged particles. The results support the prospect of developing plasma spacecharge based confinement, with an unmagnetized plasma of one species of charged particles confined by an electric field produced by an edge-confined plasma of a second species of charged particles. The Warp particle-in-cell code is used for the simulations.
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