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**Stationary Plasma Thruster ( SPT) B. Shokri**

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**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.

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**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.

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The objective of this work is related to thruster discharge to better understand the physics of Hall thruster operation and validate Hall thruster models. Present Hall thruster technology has demonstrated good performance characteristics; however, further understanding of the plasma discharge physics is required before improvements in Hall thruster technology. 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.

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**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 mission. Other electric propulsion devices are also being readied for flight, including magnetoplasmadynamic thrusters, pulsed plasma thrusters, and …

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Motivation 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.

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**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 propulsion; 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.

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**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.

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**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.

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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 device. 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.

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**Particle Motion in Uniform Fields:**

The general case of a single charged particle subject to both electric and magnetic fields will be examined.

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**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 source.

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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

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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 discharge. 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.

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**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.

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**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.

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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.

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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.

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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.

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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 مغناطيسی اندازه گيری شده در کانال تراستر با استفاده از تسلامتر

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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,

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The ionization cross section for singly ionized xenon rises from near zero at the ionization potential at eV and peaks at approximately 50 eV . The functional dependence of the ionization rate relative to electron temperature is

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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.

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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.

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But the axial plasma conductivity due to Bohm diffusion is therefore inversely proportional to the radial magnetic field.

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**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 possible. 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.

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Thrust Generation The average kinetic energy acquired by each propellant ion is a function of the potential at creation and final potential The potential difference may be better stated as the difference between the anode potential and potential lost in the propellant acceleration.

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**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.

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**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.

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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 self-consistently, 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.

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**FORMULATION OF THE PROBLEM IN A ONE-DIMENSIONAL HYDRODYNAMIC APPROXIMATION**

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.

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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

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**the model of plasma conductivity depends only on the transverse magnetic field,**

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:

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**Above equations reduce to**

and the boundary conditions and the magnetic field is taken to be

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**RESULTS OF SIMULATIONS WITH A HYDRODYNAMIC MODEL**

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. RESULTS OF SIMULATIONS WITH A HYDRODYNAMIC MODEL Time-Independent Model

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For (a) emf=400 V

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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)

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**Time-Independent Model**

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**Thrust Measurement Laser Velocimetry inverted pendulum**

Specific designed balance set

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**Specific designed balance set**

دبی گازی در حدود 2.9 ميلی گرم بر ثانيه و با تغيير ولتاژ به ترتيب جدول زير تراست دستگاه اندازه گيری شد.

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**نمودار تراست اندازه گيری شده بر حسب مقادير مختلف ولتاژ به شکل زير است**

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THE END

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