Three-Dimensional Modeling of Magnetic Nozzle Processes

Lorzel, Heath; Mikellides, Pavlos G.

doi:10.2514/1.j050123

Cited by 9 publications

(5 citation statements)

References 3 publications

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“…(21) Equation ( 19) expresses the conservation of the species electric current. The momentum equation (20), which cannot be reduced to a first integral, includes the two axial components of the pressure tensor divergence. The first one is the gradient of the parallel pressure, and the second one is the macroscopic magnetic mirror force (notice that d ln B = −d ln A), which is non-zero only if the pressure is anisotropic.…”

Section: Momentum and Energy Balancesmentioning

confidence: 99%

“…A MN uses an applied magnetic field to guide and expand a hot source plasma, and transforms its thermal energy into mechanical energy of ions through an acceleration process [10]. The conditions of the magnetized expansion have a large impact on the thrust generation efficiency, and extensive studies for its proper characterization have been conducted both experimentally [11][12][13][14][15][16][17] and theoretically [18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

“…The most common approach to model MNs is a fluid description [18][19][20][21], which allows the analysis of the expansion physics with a low computational cost. However, plasma thruster plumes are generally weakly-collisional, making it problematic to define reliable pressure tensors and heat flux closures in the fluid models.…”

Section: Introductionmentioning

confidence: 99%

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Time-dependent expansion of a weakly-collisional plasma beam in a paraxial magnetic nozzle

Zhou¹,

Sánchez‐Arriaga²,

Ahedo³

2021

Plasma Sources Sci. Technol.

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The transient and steady-state expansion of a weakly-collisional plasma beam in a paraxial magnetic nozzle is studied with a kinetic Boltzmann–Poisson model. Only intraspecies collisions involving electrons are considered and these are modeled with a Bhatnagar–Gross–Krook operator. Simulations show that occasional collisions progressively populate the phase-space region of isolated trapped electrons until a steady state is reached, which is independent of transient history. The steady state is characterized by a partial occupancy of that region increasing with the collisionality rate but far away from the full occupancy postulated by an alternative steady-state kinetic model. The changes on the amount of trapped electrons with the collisionality rate explain, in turn, the changes on the spatial profiles of main plasma magnitudes. Conclusions on the momentum and energy balances of ions and electrons agree, in terms of general trends, with those of the steady-state kinetic model. In the downstream region of the expansion, ions and electrons lose all their perpendicular energy but they still keep part of their parallel thermal energy. Electron heat fluxes of parallel energy are not negligible and are approximately proportional to enthalpy fluxes.

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Section: Momentum and Energy Balancesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Time-dependent expansion of a weakly-collisional plasma beam in a paraxial magnetic nozzle

Zhou¹,

Sánchez‐Arriaga²,

Ahedo³

2021

Plasma Sources Sci. Technol.

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“…From them, the values of the parallel and perpendicular velocities of the particles when they were injected at z=z 0 and the injection time t inj were found. The color in panel (b) of figure 11 shows the value of the electron distribution function at z=0 given by equation (18) in the v Pe −v ⊥e plane, and the red dots the region of the phase that yields trapped trajectories in the interval t inj t<t F . The figure shows that there is a single phase space region for trapped particles in the injection and it is centered about (v Pe , v ⊥e )≈ (2,2).…”

Section: Trapped Electronsmentioning

confidence: 99%

“…The modeling of magnetic nozzles has also attracted great attention. One [13], two [14][15][16][17] and three [18] dimensional fluid models have been developed, and the transformation of the internal energy of the plasma into directed kinetic energy, the plasma detachment, and the role played by the plasma-induced magnetic field have been discussed. However, since plasma flows are generally weakly collisional, simple closures of the fluid equation hierarchy for the pressure tensor and the heat fluxes are doubtful.…”

Section: Introductionmentioning

confidence: 99%

Kinetic features and non-stationary electron trapping in paraxial magnetic nozzles

Sánchez‐Arriaga

Zhou

Ahedo

et al. 2018

Plasma Sources Sci. Technol.

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The paraxial expansion of a collisionless plasma jet into vacuum, guided by a magnetic nozzle, is studied with an Eulerian and non-stationary Vlasov-Poisson solver. Parametric analyses varying the magnetic field expansion rate, the size of the simulation box, and the electrostatic potential fall are presented. After choosing the potential fall leading to a zero net current beam, the steady states of the simulations exhibit a quasi-neutral region followed by a downstream sheath. The latter, an unavoidable consequence of the finite size of the computational domain, does not affect the quasi-neutral region if the box size is chosen appropriately. The steady state presents a strong decay of the perpendicular temperature of the electrons, whose profile versus the inverse of the magnetic field does not depend on the expansion rate within the quasi-neutral region. As a consequence, the electron distribution function is highly anisotropic downstream. The simulations revealed that the ions reach a higher velocity during the transient than in the steady state and their distribution functions are not far from mono-energetic. The density percentage of the population of electrons trapped during the transient, which is computed self-consistently by the code, is up to 25% of the total electron density in the quasi-neutral region. It is demonstrated that the exact amount depends on the history of the system and the steady state is not unique. Nevertheless, the amount of trapped electrons is smaller than the one assumed heuristically by kinetic stationary theories.

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Feedback control of a spacecraft electro-dynamic thruster

Vepa

2020

Acta Astronautica

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In this paper, the possibility of feedback servo control of a spacecraft thruster's specific impulse by a boundary feedback system is theoretically considered. The motivation to introduce feedback control is two-fold. The first is to stabilize any inherent plasma instabilities and the second is regulate the output specific impulse of the thruster. Two cases are considered: Electro-thermal thrusters and Electro-dynamic thrusters. The chamber inlet temperature in the case of the electro-thermal thruster or the boundary electric field potential responsible for generation of the velocity of the plasma ions in the case of an electrodynamic thruster, are controlled by feedback so as to regulate the thruster's specific impulse. By introducing typical disturbances in the plasma ionization voltage, it is shown using a two-dimensional fluid model and a suitable boundary feedback law, where the chamber inlet temperature or applied boundary potential is proportional to the error in the specific impulse and the desired specific impulse, that the specific impulse of the thruster may be regulated and held constant. The robustness of the control system is numerically tested, by a two dimensional simulation model using McCormacks's method. The Navier-Stockes equations, including the magneto-hydrodynamic variables were discretized and simulated, using the explicit MacCormack method for a typical nozzle domain. The numerical results for the open and closed-loop velocity fields were obtained and the specific impulse was computed from these fields. It was thus shown that not only the stability of the plasma is realised but also that the specific impulse is regulated as desired.

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Three-Dimensional Modeling of Magnetic Nozzle Processes

Cited by 9 publications

References 3 publications

Time-dependent expansion of a weakly-collisional plasma beam in a paraxial magnetic nozzle

Time-dependent expansion of a weakly-collisional plasma beam in a paraxial magnetic nozzle

Kinetic features and non-stationary electron trapping in paraxial magnetic nozzles

Feedback control of a spacecraft electro-dynamic thruster

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