Steady state densities in a plasma confined by a dipole magnet: Diffusion induced transport explored through direct measurements and modeling

Abstract

Steady state densities in a plasma confined by a permanent dipole magnet are determined through detailed experiments and modeling. Two diffusion models are developed, and the resulting equations are solved numerically to yield the radial and angular plasma density profiles, which are compared with those obtained experimentally. The models consider the fluid and continuity equations along with Fick’s law and take into account the experimentally determined electron temperature (Te) and the static dipole magnetic fields (B) in space, as a common input. In model I, the equation of motion for both charges (ions and electrons) is used to self-consistently generate the ambipolar electric field (E), while model II considers the electron equation of motion and takes into account the experimentally determined plasma potential (Vs) as another input, whose gradient provides the ambipolar electric field. Results indicate that the plasma density peaks around r ∼ (2–12) cm depending on the polar angle and the discharge pressure and decreases for large r, while its angular variation shows a maximum in the equatorial plane (θ = 90°) and decreases toward the polar regions. Te and Vs are higher in the polar cusp regions and decrease toward the equatorial plane, with the profiles becoming more spherically symmetric away from the magnet. The numerically obtained density profiles from the models agree well with those obtained experimentally. The phenomenon of inward diffusion resulting in peaked density profiles as reported by earlier authors is found to be a natural outcome of the solution of the diffusion equation.

Characterizing spatially varying optical emissions in a steady-state dipole plasma: inversion based experiments and modeling

“…Although the pressure and magnetic field intensities are quite different for this experiment, we observe that these regions show structural resemblance to the Earth's Van Allen radiation belts, whose underlying mechanisms are still not completely well understood [8]. While basic plasma parameter diagnostics, such as those of density and temperature, have been performed in most earlier works [9][10][11], a characterization of the optical emissions has not been performed yet in such plasmas to the best of our knowledge. This may be attributed to motivational differences and/or engineering challenges.…”

“…The periodic minor rise and fall of local emissivities every ∼ 0.5 cm in the results is best attributed to experimental artefact as the spatial resolutions of our experiments were exactly 0.5 cm. Given these experimental results, we now attempt to verify the results via theoretical modeling wherein we will employ the electron number densities and temperature measurements from previous studies [4,9,10] to determine the wavelength-specific photon emission rates in the dipole plasmas of both systems Exp 1 and Exp 2.…”

“…The plasma is confined inside VC in a dipole magnetic field, created by using a single, cylindrical permanent magnet (material: NdFeB, grade: N40) having length 4.1 cm and diameter 2.3 cm. Detailed experimental mapping of the magnetic field has been carried out at various polar angles and distances from the magnet [4,9,10]. The magnet is kept at the center of VC with the help of a magnet holder which includes the cooling jacket assembly and is thus further connected to a water chiller (model: Equitron 4.0 L) for water inlet and outlet (for further details, see [4]).…”

“…, where ò 0 is the vacuum permittivity, and the plasma parameters were determined using equations ( 5)-( 7), giving n e ∼ 1.7 × 10 16 m −3 [10], T e ∼ 3.5 eV, n i ∼ 7 × 10 17 m −3 [9], and T i ∼ T e /10 = 0.35 eV [10], and we obtain λ D ∼ 5.25 μm. The extensible arm was kept grounded during its insertion into the plasma.…”

“…Due to the lack of data on the pressure dependence of these cross-sections (which is expected to be weak [31]), these cross-sections were used uniformly at both pressures in the systems. Thus, we evaluate the corresponding optical cross-sections using equation (10), wherein, the branching fractions can be evaluated using the transition probabilities available in the NIST database [25], and verified from [32].…”