PhyThematics 19 – Magnetic shielding in Hall Thrusters

Hall thrusters operate based on the principle of electron confinement. The fundamental objective is to confine electrons using magnetic fields so they can ionize neutral propellants and thus create and sustain a plasma. The ions formed are then accelerated out of the thruster by an electric field to produce thrust.

Thruster Life and Magnetic Field: The thruster lifetime is strongly influenced by the topology of the magnetic field, particularly the placement of the lens. Erosion shortens the thruster’s life due to problems such as divergence from equipotentials and the creation of plasma sheaths close to the thruster’s walls.

Magnetic Protection: The problem of ceramic wall degradation in Hall thrusters is addressed by this technique. The lifetime of a thruster can be significantly increased by altering the magnetic field topology. Effective magnetic shielding requires a “grazing line” tangent to the wall near the exit that penetrates deeply. By creating an electric field that keeps ions from penetrating the wall, this arrangement lessens erosion.

REFS:

[1] Maryam Reza, Eugenio Ferrato, Farbod Faraji, Tommaso Andreussi, Mariano Andrenucci, “Magnetic Circuit Optimization for Hall Thrusters Design”, IEPC-2019-A459 Presented at the 36th International Electric Propulsion Conference, University of Vienna • Vienna, Austria, September 15-20, 2019

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PhyThematics 17 – The Zakharov-Kuznetsov equation and its applications

The Zakharov-Kuznetsov (ZK) equation is a partial differential equation that describes the evolution of weakly nonlinear dispersive waves in two spatial dimensions. The equation was introduced by V.E. Zakharov and E.A. Kuznetsov in 1972.

The Korteweg-de Vries (KdV) equation, which explains the development of one-dimensional weakly nonlinear dispersive waves, is generalized by the ZK equation. The ZK equation may be used to examine two-dimensional waves since it has an extra element that takes into consideration the coupling between waves moving in the x and y axes.

Some intriguing characteristics of the ZK equation include the existence of soliton solutions and the potential for wave breaking. It is often employed in the research of many different physical phenomena, such as fluid dynamics, nonlinear optics, and plasma physics.

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Some codes in python or python notebooks will be available here on GitHub: https://github.com/mjgpinheiro/Physics_models

Phythematics 14-The Railgun as a launcher hypersonic system

A railgun or rail gun is a linear motor device, typically designed as a weapon, that uses electromagnetic force to launch high velocity projectiles. The projectile normally does not contain explosives, instead relying on the projectile’s high speed, mass, and kinetic energy to inflict damage.^[2] The railgun uses a pair of parallel conductors (rails), along which a sliding armature is accelerated by the electromagnetic effects of a current that flows down one rail, into the armature and then back along the other rail. It is based on principles similar to those of the homopolar motor.^[3] – Wikipedia.

REFS: See References given in the text.

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Phythematics 11-Resultant force acting on a Hall thruster

«Hall thrusters are able to accelerate their exhaust to speeds between 10 and 80 km/s (1,000–8,000 s specific impulse), with most models operating between 15 and 30 km/s. The thrust produced depends on the power level. Devices operating at 1.35 kW produce about 83 mN of thrust.» – Wikipedia

REF:https://descanso.jpl.nasa.gov/SciTechBook/series1/Goebel__cmprsd_opt.pdf

[1] Fundamentals of Electric Propulsion: Ion and Hall Thrusters, Dan M. Goebel and Ira Katz [and correcting a typo on page 18]

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Phythematics 9-Breathing mode in Hall Thrusters

Breathing mode is an ionization instability which is observed ubiquitously in the operation of Hall thrusters. It is recognized as a relatively low frequency (10–30 kHz) longitudinal oscillation of the discharge current and the plasma parameters.

REF:

[1] Anode sheath in Hall thrusters, Appl. Phys. Lett. 83, 2551 (2003); https://doi.org/10.1063/1.1615307

L. Dorf and V. SemenovInstitute of Applied Physics of Russian Academy of Science, Nizhny Novgorod, Russia 603155

Y. RaitsesPrinceton Plasma Physics Laboratory, Princeton, New Jersey 08543

[2] O. Chapurin, A. I Smolyakov, G. Hagelaar, Y. Raitses. On the mechanism of ionization oscillations in
Hall thrusters. Journal of Applied Physics, American Institute of Physics, 2021, 129 (23), pp.233307.
￿10.1063/5.0049105

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Phythematics 6-Hall Thrusters

Hall thrusters are essential for control attitude of artificial satellites and spacecrafts.

REF: Dan M. Goebel and Ira Katz, Fundamentals of electric Propulsion-ion and Hall thrusters (John Wiley & sons, New Jersey, 2008)

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