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Stationary Plasma Thruster ( SPT)
B. Shokri
‫به نام خدا‬
• This talk is devoted
• first to the development of stationary plasma thrusters,
which have operated for thirty years on 30 satellites for
the current problems of astronautics.
• Second to the importance of the physical results
obtained in the course of the development of stationary
plasma thrusters (SPTs) for the general problems of
plasma dynamics and various practical applications.
Plasma physics is faced, among others, with three
great problems:
(i) controlled nuclear fusion,
(ii) MHD generators capable of substantially
increasing the efficiency of thermoelectric power
stations, and
(iii) space plasma thrusters.
• The objective of this work is related to
discharge to better understand the physics of Hall
thruster operation and validate Hall thruster models.
Present Hall thruster technology has demonstrated good
understanding of the plasma discharge physics is
required before improvements in Hall thruster
• Here, the results of a thorough analysis of the model are
presented and are compared with the experimental data
in the range of working parameters of an SPT.
Electric Propulsion Fundamentals
• 40 years after the first orbital flights of Sputnik and
Explorer, electric propulsion is a viable alternative to
chemical spacecraft propulsion.
• An ion engine has powered a NASA deep space flight
• Other electric propulsion devices are also being readied
for flight, including magnetoplasmadynamic thrusters,
pulsed plasma thrusters, and …
• Clearly, it is necessary to increase the exhaust velocity.
Among thermochemical engines, oxygen–hydrogen
engines provide the highest flow velocity (~4.5 km/s),
which is too low for long-range flights. The switching to
engines with high exhaust velocities requires external
energy sources. In space, energy (solar or nuclear) is
cheaper than mass; hence, such a change is justified.
Moreover, for every expedition, there is an optimal
exhaust velocity at which the total mass of the working
material and the energy system is minimal. At present,
the optimal exhaust velocities are 15–30 km/s for most of
the tasks, and it is SPTs that cover this range.
• In July 1959, the idea of generation of ion and plasma
flows was suggested to draw more attention to the
problem of electric propulsion. Finally a gasdynamic
nozzle (A.I. Morozov) got more attention.
Electric Propulsion Fundamentals
Electric propulsion in its most general sense can be defined as; “The
acceleration of gases for propulsion by electrical heating and/or by electric
and magnetic body forces.” There are three main categories of electric
Electrothermal: In these devices, the propellant gases are electrically
heated and then expanded to produce thrust. An example of this
classification is the arcjet in which the propellant is heated by an arc
between two electrodes and subsequently expanded through a nozzle.
Electrostatic: In these devices, the propellant is first ionized and the
resulting ions are then accelerated by direct application of electric body
forces. The classic example of an electrostatic thruster is the ion, or
Kaufman engine
Electromagnetic: In electromagnetic devices, ions are accelerated by the
combination of electric and magnetic fields producing Lorentz forces which
exert an electromagnetic force on the propellant. An example of an
electromagnetic thruster is a magneto-hydro-dynamic channel in which an
applied current and an orthogonal magnetic field produce a propellant
accelerating force.
Electric Propulsion Fundamentals
• The principle advantage of electric propulsion over
traditional chemical propulsion is that electric propulsion
is not limited in its propellant energy release. Chemical
systems rely on the energy released from chemical
bonds to produce thermal energy that is then converted
into propulsive thrust by expansion through a nozzle.
Electric thrusters have no limitation on the amount of
energy that may be deposited into the propellant. Since
electric thrusters require electrical energy, the
engineering trade off is that thrust levels are limited by
electrical power. Following table shows the specific
impulse ranges for the several general types of chemical
and electric thrusters.
Electric Propulsion Fundamentals
• Due to their much higher specific impulses, electric
thrusters are capable of using significantly less
propellant mass to produce the same impulse as
chemical thrusters, thereby enhancing spacecraft
capabilities and reducing life cycle costs. The high
specific impulse of electric propulsion is not without
penalties. However electric propulsion is generally
limited to a low thrust level. Low thrust, high specific
impulse applications include satellite station-keeping,
repositioning, and attitude control.
Plasma parameters
• In order to provide better understanding of Hall thruster
physics, measurements of three plasma parameters
are important.
• Velocity is the most important plasma parameter in an
electric thruster. The thrust produced is directly
proportional to the exhaust velocity.
• Since Hall thrusters are electro-static plasma
accelerators, the velocity and acceleration of the ionized
propellant depend on the electric fields produced by the
• The final critical parameter essential for understanding
Hall thruster physics is electron temperature. Electron
temperature data provide information on the ionization
rate of the propellant and an indication of the electron
mobility within the magnetic field.
Particle Motion in Uniform Fields:
E  0, B  0
• The general case of a single charged particle subject to
both electric and magnetic fields will be examined.
Hall Thruster Physics
General Operating Features
• Hall thrusters function uses perpendicular electric and
magnetic fields. The radial magnetic field acts to impede
the flow of electrons from cathode to anode. The
electrons are trapped near the exit of a coaxial
acceleration channel. The crossed fields produce a net
Hall electron current. The trapped electrons act as a
volumetric zone of ionization for neutral propellant
atoms. Electrons collide with the slow moving neutrals
producing ions and more electrons to both support the
discharge and ionize additional neutrals. The positive
ions are not significantly affected by the magnetic field
due to their larger Larmor radii, which are on the order of
meters. The ions are accelerated through the electric
field produced. The resulting high speed ion beam is
subsequently neutralized with an external electron
Hall Thruster Physics
• Therefore, Hall thruster is an electrostatic accelerator
where thrust is produced by momentum imparted to the
positive ions by electric body forces. The thruster is
relieved of space charge limitations by the neutralizing
effect of the trapped electrons. Due to the crossed
electric and magnetic fields within a Hall thruster, a
sizable azimuthal Hall current is produced. A coaxial
geometry is used to short the Hall current, and the
electrons are confined in an endless azimuthal drift.
• The typical geometry and sizing of Hall thrusters have
not changed significantly since the earliest work reported
on Hall type plasma accelerators
Hall Thruster Physics
• The plasma discharge within a Hall thruster requires an
anode and a cathode. The anode serves two purposes.
First, it is the positive electrode supporting the plasma
• Second, it distributes the propellant gas through the
coaxial acceleration channel.
• The cathode provides an electron source to both support
the electric discharge and neutralize the ion beam.
Hall Thruster Physics
• Hall thruster has two classes as:
• stationary plasma thrusters (SPT), an electrical
insulator isolates the anode from the magnetic circuit. It
also directs the propellant into the volume where the
neutral propellant is ionized, accelerated, and expelled
from the thruster.
• anode layer thrusters (ALT) do not have dielectric
insulators. These thrusters have the magnetic circuit in
direct contact with the plasma.
Impact of the Magnetic Field
• The magnetic field is the single most important
parameter in the design of a Hall thruster. The
concentration of electrons in a Hall thruster depends on
the Larmor radius. For electrons with little, or no,
directed velocity, a value for can be approximated from
the electron mean thermal speed.
• In order to constrain the electrons and allow the ions to
be accelerated by the electric field within a Hall thruster,
the electron Larmor radius must be smaller than the
width of the acceleration channel. Conversely, the ion
Larmor radius must be significantly larger, such that the
magnetic field does not affect the trajectory of the ions
as they accelerate through the axial potential fall.
• The electron Larmor radius depends only on the
magnetic field strength and the electron temperature.
Typically, the ions have a temperature near 1 eV, and the
magnetic field is on the order of 150 G, and the Larmour
radii are approximately 50 cm and 1 mm for the ions and
electrons, respectively. In regard to the ion Larmour
radius, the large mass of xenon (131 amu) compared to
other inert propellant gases such as argon (40 amu) and
krypton (84 amu) is important factor.
• An important limitation of Hall thruster efficiency
is the magnitude of the axial electron current. To
limit this loss mechanism, the anode is placed
far from locations of high electron density where
the magnetic field has confined electrons.
Typical magnetic circuits produce radial
magnetic field profiles with Gaussian functions.
Therefore, the following conditions for the
magnetic field profile and length of the
acceleration channel hold.
• The effects of magnetic field shape has been explored
experimentally by Morozov et al. who showed that the
profile of the radial magnetic field has a strong effect on
the performance of a Hall thruster.
‫پروفايل ميدان مغناطيس ی اندازه‬
‫گيری شده در کانال تراستر با‬
‫استفاده از تسالمتر‬
Ionization Processe
• The Hall thruster is an electrostatic accelerator, and for
the propellant to be accelerated, it must first be ionized.
The neutral-electron collisional ionization rate is given by
the following.
Where g is the relative speed of collision,
• The ionization cross section for singly ionized xenon
rises from near zero at the ionization potential at 12.127
eV and peaks at approximately 50 eV . The functional
dependence of the ionization rate relative to electron
temperature is
• The thrust produced by the propellant is given by the
exiting momentum which can be divided into the
fractions produced by the ions and neutrals.
Electric Field
• Early Hall thruster studies showed that the
electron current across the radial magnetic field
of a Hall thruster is significantly higher than
predicted by classical electrodynamic theory.
This greater than predicted electron diffusion
across magnetic field lines is now often referred
to as Bohm diffusion. The classical conductivity
of a plasma across a magnetic field is inversely
proportional to the square of the magnetic field.
• But the axial plasma conductivity due to Bohm diffusion
is therefore inversely proportional to the radial magnetic
Insulator Wall Effects
• In order to minimize this loss mechanism, the ionization
region must lie close to the exit plane and be as short as
• The atoms and ions have a larger probability of striking
the dielectric walls than of a collision with another atom,
or ion. Neutrals striking the walls will reflect diffusely at
the ground state energy. Ions that strike the wall will
recombine on the wall surface and leave the surface
diffusely at the atomic ground energy state.
Thrust Generation
• The average kinetic energy acquired by each propellant
ion is a function of the potential at creation and final
• The potential difference may be better stated as the
difference between the anode potential and potential lost
in the propellant acceleration.
Hall Thruster Instabilities
• The nature of the instabilities that give rise to the
unsteady behavior in Hall thrusters at relatively low
thrusters is strongly dependent on the sign of the axial
gradient in the applied magnetic field.
• There appear to be at least three principle oscillatory
modes present in Hall thrusters.
Formulation and simulation
• The rather specific features of the processes occurring in
a stationary plasma thruster (SPT) stem from the strong
interaction between the plasma electrons and the
dielectric walls of the channel. This interaction governs,
the electron distribution function (EDF) as well as
electron transport along the channel (the conductivity of
the wall plasma), and thereby the electric field
distribution, and influences the ionization rate and the
rate at which the atoms and ions are excited. The
electron kinetics, in turn, is governed by the rate
coefficients for the secondary electron emission from the
walls, the evolution of Debye sheaths and the
conductivity of the wall plasma.
• The processes in the SPT channel can be described
systematically only by using kinetic models for atoms,
ions, and electrons. However, such a self-consistent
description seems to be too sophisticated. However, It is
possible to study the ion and electron dynamics selfconsistently, but in the hydrodynamic (or, at most, hybrid)
approximation under special assumptions for linear
waves . A one-dimensional set of hydrodynamic
equations is set to describe the atom and ion dynamics
self-consistently and including an integral equation for
the discharge circuit.
• Basic Equations
• It is clear that a complete self-consistent model of the
processes in an SPT will be extremely complicated.
Hence, we begin with a one-dimensional hydrodynamic
model of the dynamics of electrons, atoms, and ions. We
restrict ourselves to consider only singly charged ions.
• We direct the x-axis along the channel so that x=0 is the
anode surface and the channel end x=L is the cathode
surface. The main parameters in our model are the ion
density, the electron density being the same by virtue of
plasma quasineutrality), the ion Velocity V, the neutral
density n_a, and the electric current J in the system.
• The model set of quations consists of the ion continuity
equation, the equation of ion motion Ohm’s law the
continuity equation for atoms and the equation for the
electric circuit
• the model of plasma conductivity depends only on
the transverse magnetic field,
 H0 
 ,  0  const ,
 x    0 
 H x  
H 0  const ,
• Above equations are investigated under fairly
arbitrary initial onditions and are supplemented with
the following time-independent boundary conditions
at the anode surface x= 0:
Above equations reduce to
and the boundary conditions
n nV
 vnna ,
nV 2
 nE  vnnaVa ,
E  h 2  x  J  nV ,
n a
n a
 Va
 vnna ,
 rJ   Edx  1
n0, t   n0 , na 0, t   1, V (0, t )  1
and the magnetic field is taken to be
hx   h0  1  h0 x 2 , h0  H 0 H 0 .
The boundary-value problem for equations which
contain a nonlocal term, is highly nonlinear and
involves a number of parameters. Presumably, the
problem can be investigated more or less completely
only by solving equations (8) numerically using
computer codes.
We consider a practically important range of the SPT
parameters, such that the mass flow rate is = 2– 4
mg/s and the discharge voltage is U0 = 200–400 V, the
working gas being Xe.
• Time-Independent
For (a) emf=400 V
• In order to analyze the stability of steady solutions
derived above, we can regard them as initial conditions
for time-dependent equations.
• By varying the channel resistivity and fixing the
remaining parameters, a steady stable solution in the
range of sufficiently low resisitivity value appears .
• By increasing the channel resistivity this solution became
unstable at the certain value of resistivity. This solution
becomes unstable and a periodic solution appears.(a)
• A further increasing in resistivity results in a solution
describing unsteady aperiodic (stochastic) regimes(b)
Time-Independent Model•
Thrust Measurement
• Laser Velocimetry
• inverted pendulum
• Specific designed balance set
‫‪Specific designed balance set‬‬
‫دبی گازی در حدود ‪ 2.9‬ميلی گرم بر ثانيه و با تغيير ولتاژ به ترتيب جدول زير تراست‬
‫دستگاه اندازه گيری شد‪.‬‬
‫• نمودار تراست اندازه گيری شده بر حسب مقادير مختلف ولتاژ به شکل زير است‬