Conditions and growth rate of Rayleigh instability in a Hall thruster under the effect of ion temperature

Journal Article · Tue Mar 15 04:00:00 EDT 2011 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)

DOI:https://doi.org/10.1103/PHYSREVE.83.036406· OSTI ID:21560079

Malik, Hitendra K; Singh, Sukhmander ^[1]

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1. Plasma Waves and Particle Acceleration Laboratory, Department of Physics, Indian Institute of Technology Delhi, New Delhi 110 016 (India)

Rayleigh instability is investigated in a Hall thruster under the effect of finite temperature and density gradient of the plasma species. The instability occurs only when the frequency of the oscillations {omega} falls within a frequency band described by k{sub y}u{sub 0}+(1/k{sub y})({partial_derivative}{sup 2}u{sub 0}/{partial_derivative}x{sup 2})+({Omega}/k{sub y}n{sub 0})({partial_derivative}n{sub 0}/{partial_derivative}x)<<{omega}<{radical}((Y{sub i}T{sub i}k{sub y}{sup 2}/M)+({omega}{sub pi}{sup 2}({Omega}{sup 2}+Y{sub e}T{sub e}k{sub y}{sup 2}/Y{sub e} T{sub e}k{sub y}{sup 2}mm)/({omega}{sub pe}{sup 2}+{Omega}{sup 2}+Y{sub e}T{sub e}k{sub y}{sup 2}/Y{sub e}T{sub e}k{sub y}{sup 2}mm))), where u{sub 0} is the drift velocity of the electrons, {Omega} is their gyration frequency under the effect of the magnetic field, k{sub y} is the wave propagation constant, n{sub 0} is the plasma density together with {partial_derivative}n{sub 0}/{partial_derivative}n{sub 0}{partial_derivative}x{partial_derivative}x as the density gradient, and T{sub i}(T{sub e}), M(m), Y{sub i}(Y{sub e}), and {omega}{sub pi}({omega}{sub pe}) are the temperature, mass, specific heat ratio, and plasma frequency of the ions (electrons), respectively. A relevant Rayleigh equation is derived and solved numerically using the fourth-order Runge-Kutta method for investigating the perturbed potential under the effect of electron drift velocity, channel length, magnetic field, ion temperature, and electron temperature. The instability grows faster because of the magnetic field, ion temperature, and drift velocity of the electrons but its growth rate is reduced because of the electron temperature, channel length, and also its far distances from the anode.

• OSTI ID: 21560079
• Journal Information: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print), Journal Name: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print) Journal Issue: 3 Vol. 83; ISSN 1539-3755
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
ANODES
CALCULATION METHODS
ELECTRODES
ELECTRON DRIFT
ELECTRON TEMPERATURE
ELECTRONS
ELEMENTARY PARTICLES
FERMIONS
INSTABILITY
ION TEMPERATURE
ITERATIVE METHODS
LANGMUIR FREQUENCY
LEPTONS
MAGNETIC FIELDS
MATHEMATICAL SOLUTIONS
NUMERICAL SOLUTION
OSCILLATIONS
PHYSICAL PROPERTIES
PLASMA
PLASMA DENSITY
POTENTIALS
RAYLEIGH-TAYLOR INSTABILITY
RUNGE-KUTTA METHOD
SPECIFIC HEAT
THERMODYNAMIC PROPERTIES
THRUSTERS
VELOCITY
WAVE PROPAGATION