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Operation analysis of pulsed plasma thruster
Acta Astronautica 62 (2008) 404 – 409 www.elsevier.com/locate/actaastro
Operation analysis of pulsed plasma thruster Hou Dali∗ , Zhao Wansheng, Kang Xiaoming School of Mechanical Engineering, ShangHai Jiao Tong University, No. 800, Dongchuan Rd., ShangHai 200030, China Received 3 January 2007; accepted 8 January 2008 Available online 14 February 2008
Abstract Pulsed plasma thruster (PPT) is an attractive micro-thruster for many flight missions. Compared to other electric propulsion systems, PPT is more compact, lightweight and robust while lower in thrust efficiency. It is very difficult to solve this problem because of lacking of theoretically thorough understanding of the energy transformation. In this paper, an attempt was made to explain the process from a different viewpoint where the acceleration is divided into two stages based on the dominative status. At the beginning of discharge, the electrothermal acceleration is primarily near the propellant surface. In the second stage, ions and electrons are accelerated by the electromagnetic field induced by the discharge between the electrodes. Electromagnetic acceleration contributes substantially to the thrust. Some measures should be taken to ameliorate the electrothermal acceleration at the first stage and enhance the electromagnetic acceleration at the second stage. For the purpose of improving thrust efficiency, the relations between the acceleration and electrode gap, electrode width, discharge energy have been discussed. Some methods by modifying design parameters are presented to enhance the accelerating effect. © 2008 Elsevier Ltd. All rights reserved. Keywords: Pulsed plasma thruster; Thrust; Specific impulse; Thrust efficiency
1. Introduction Pulsed plasma thruster (PPT) is an electric propulsion device using electric power to ionize and electromagnetically accelerate plasma to high exhaust velocity. PPT has a broad prospect on small satellites. It has many features which make the PPT more attractive than traditional propulsion. Firstly, the PPT offers a high specific impulse compared to other micro-thrusters. Typically its specific impulse ranges from 800 to 1200 s. Secondly, PPT is small, robust, compact and low mass. As the spring is the only removable part, the structure of PPT is of higher reliability than other systems. Using Teflon as its propellant allows significant reductions ∗ Corresponding author. Tel./fax: +86 21 6293 4959.
E-mail address: [email protected] (H. Dali). 0094-5765/$ - see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.actaastro.2008.01.004
in mass and volume of the thruster by eliminating the propellant tankage and valves [1]. Thirdly, PPT operates at low power level and its pulsed nature permits operation over a relatively broad power range without loss of performance. Power supply is generally below 100 W. The low power level is fit for small satellites and can regulate the power supply by changing the discharge frequency. For example, when changing the discharge frequency from 1 to 0.01 Hz, the power level can be reduced to 1% of its original power level. Thus, the mass of power supply is reduced, thereby reducing the launching cost of the satellites. Lastly, the impulse bit is low; it ranges from tens to hundreds of N s. PPT can provide both impulse force and continued force. Continued force can be regulated easily by varying the discharge frequency. The PPT is extremely flexible and can easily be customized to meet propulsion
H. Dali et al. / Acta Astronautica 62 (2008) 404 – 409
requirements for a wide variety of missions. For this reason, it has been used in attitude control, orbit distracting and drag compensating, etc. For example, in attitude control system, PPT provides stabilization instead of reaction wheels only needing lower cost, lower mass and power requirements [2]. However, the overall efficiency of PPT is very low, that limits its application in some conditions. The PPT for the LES8/9 has a thrust efficiency of 7% and the PPT of EO-1 is about 8%. The efficiency of PPT reported in recent years is rarely exceeds 10%. The reasons are listed as follows. Firstly, PPT is inefficient when transferring stored capacitor energy into acceleration of the ionized propellant. Secondly, mass utilization efficiency in PPT is low (< 50%) because of two performance robbing processes—late-time vaporization [3] and macro-particles ejection. Many propellant particles are wasted in the form of propellant vapor and large chunks. The thrusters have very low efficiency due to a combination of poor energy coupling into the propellant, late-time ablation, and inefficient acceleration. The study of plasma accelerations is very important to solve the lower thrust efficiency. In this paper, the process from discharge to thrust generation is described and a new idea to understand the acceleration theory is provided. It is very helpful to design a high efficient PPT. 2. Fundamentals The PPT systems are completely self-contained propulsion modules. Generally, it includes a power source, a power processing unit (PPU), an energy storage unit, and the thruster itself. Solar cells are generally used as power sources, since the thruster operates at a low power level. The main functions of the PPU are to provide the charging voltage for the energy storage unit and to provide the command and telemetry functions required to operate the PPT. The energy storage unit provides high-current pulses through the thruster to perform work. Capacitor is often used as an energy storage unit. Thruster typically consists of two electrodes, the propellant, a negater spring and a spark plug. The configuration of PPT is illustrated in Fig. 1. At the beginning of PPT operation, the capacitor is charged to the desired voltage. The spark plug is ignited to trigger the discharge. The energy stored in the capacitor powers a high-current duration plasma discharge and produces an electromagnetic field. Then the molecules of propellant are ionized. Due to the actions of a J × B electromagnetic Lorentz force and gas-expanding force,
405 Spark Plug Cathode
Propellant
Plasma
Anode Capacitor
+
PPU
-
Fig. 1. Basic schematic of PPT.
the plasma is accelerated to high exhaust velocities and thrust is generated. 3. Discussion For the purpose of improving the efficiency of PPT, the related theory is studied to increase mass utilization efficiency and power efficiency. The crucial difficulty in PPT modeling is lacking of theoretically thorough understanding of the process of energy transfer from discharge to solid propellants and mass ablation. The electromagnetic and thermal phenomena involved in propellants acceleration are very complicated. There is still no physical model to accurately predict the behavior of the thruster. Generally, there are two types of acceleration mechanisms employed in PPT which are electromagnetic acceleration and electrothermal acceleration [4]. In the electrothermal acceleration stage, the thrust is produced by gas expansion which is caused by discharge. In the electromagnetic acceleration stage, a thrust is produced by accelerating ionized particles in the electric field and the self-induced magnetic field. The thrust of PPT is defined as [5] T = TEM + TET
(1)
with TEM the electromagnetic force and TET the thrust contributed by the gas dynamic expansion, i.e. the electrothermal force. TEM is expressed by 0 h t 2 i dt, (2) TEM = f 2 w 0
406
H. Dali et al. / Acta Astronautica 62 (2008) 404 – 409
where f is the pulse frequency, i is the total current calculated by RLC circuit analysis, 0 is the magnetic permeability, h is the gap between the electrodes, w is the width of the electrodes and l is the length of the electrodes. TET is given by 1/2 8( − 1) TET = f 2 ·m·E , (3) ( + 1) where m is the mass loss per impulse and is a constant decided by the propellant materials. For Teflon, = 1.3. E is the total energy of PPT discharge. To achieve the best PPT performance, it is necessary to improve the electromagnetic force and the gas-expanding force. Thus, it is very important to understand the acceleration. At the beginning of discharge, the spark plug is ignited by a high voltage. Some electrons are produced and impact the surface of the propellant with a high velocity. The particles include ions, electrons and neutral particles escaping from propellant. With the effect of strong electric field between cathode and anode, these ions are accelerated and keep on impacting the propellant. Plasma comes into being between the electrodes for the reason of the frequent collisions between particles (including electrons, ions and neutral particles) and propellant. The compositions of this plume are carbon, fluorine, and a variety of fluorocarbons including CF3 , CF2 , and CF [6]. It is difficult to explain the complicated electromagnetic and thermal phenomena involved in propellants acceleration. Firstly, the electrothermal acceleration occurs near the propellant surface where the discharge happens. Once the plasma forms, the electrodes become conductive and main discharge occurs. The discharge ablates the propellant and produces more particles, which makes the pressure near the propellant surface increases greatly. A part of the power transfers into heat and increases the temperature of plasma. This makes the pressure of PPT chamber increase rapidly. Particles are then accelerated by the high pressure in the chamber of the PPT. This is the first stage of acceleration, i.e. electrothermal acceleration. This acceleration is mainly induced by thermal energy generated by discharge. In this stage, particles have not entered into the electric field and there is no electromagnetic acceleration. The density of the plasma is low and can be regarded as rarefied plasma. The relation of the pressure, volume and temperature for rarefied plasma is described by Clapeyron equation P V = nR 0 T ,
(4)
where P represents the pressure of plasma, V is the volume of PPT chamber, T is the temperature of plasma, n is the quantity of mole and R0 is a constant expressed by R0 = 8.314 J/mol K.
(5)
Late-time vaporization happens in this stage. Even though in electrothermal PPT which mostly thrust comes from electrothermal acceleration, up to 70% of propellant can reach acceleration channel of the thruster after the main discharge finish or at the moment of considerable discharge current drop [7]. To make more particles reach the acceleration channel, the pressure of plasma should be increased. From Eq. (4), increasing the temperature of plasma is an effective way. The high energy of discharge is used to increase the thermal energy. The temperature rises and the thrust correspondingly increases. The temperature should not be too high after discharge otherwise it will cause more particles escaping from propellant which makes low mass utilization efficiency. Macro-particles are believed to be ejected from the propellant and electrode surfaces as a result of local overheating thereby leads to low propellant efficiency [8]. This part of propellant loss produces a negligible thrust because of the low particle velocity (< 3 km/s). The other way round, keeping propellant temperature low after discharge will realize a significant savings in propellant mass. Improving the quantity of particles i.e. n in Eq. (4) is an efficient method to increase the thrust. Enlarging exposed area of the propellant is often adopted to improve the thrust. Decreasing the chamber volume near the propellant surface is another method. This is the reason why many electrothermal PPTs have very small volume at the end of the chamber. In the second stage, electrothermal accelerated particles enter into the electric field. The gas-expanding effect becomes weaker when particles are far away from the surface of the propellant. The neutral particles are not affected by electric field and cannot be accelerated. Previous researches have concluded that as little as 10% of the consumed propellant is converted to plasma and efficiently accelerated to a high velocity by electromagnetic forces [1]. It is about 90% of the propellant, i.e. neutral particles can not get an electromagnetic acceleration. Thus, the existence of neutral particles is an important reason for the low efficiency of PPT. In this stage, the charged particles achieve high velocity. Although those particles have less mass than neutral particles, they contribute much more to the momentums. Therefore, the electromagnetic acceleration is very important for the PPT performance. Neutral particles take
H. Dali et al. / Acta Astronautica 62 (2008) 404 – 409
407
SPARK PLUG CATHODE
B
F PROPELLANT
PLASMA
B
THRUST
V
V
F
ANODE
Fig. 3. Lorentz forces of ions and electrons in magnetic field.
SPARK PLUG ELECTROTHERMAL ACCELERATION
ELECTROMAGNETIC ACCELERATION
CATHODE 1
Fig. 2. Schematic of acceleration stage. PROPELLANT
most of mass but get no electromagnetic acceleration because of lacking electric charge. This poor mass utilization represents a main factor to the low efficiency of PPT. Nowadays, studies on improving thrust efficiency area mainly focused on ameliorating the electromagnetic acceleration and decreasing the amount of neutral particles. Fig. 2 is the illustration of the acceleration process. In order to analyze the electromagnetic acceleration, the behavior of charged particles in magnetic field should be studied. The Lorentz force law is described as f = qE + qv × B.
(6)
It gives the definition of the force acting on a charge q moving with velocity v in an electric field E and a magnetic field B. The magnitude of the magnetic force exerts on a moving unit charged particle is the product of the particle’s charge, its velocity and the magnetic flux density. The initial charged particle velocity is a result of the electrothermal acceleration. The Lorentz force is perpendicular to both the velocity v of the charge q and the magnetic field B. The magnetic force on a stationary charge or a charge moving in parallel to the magnetic field is zero. The Lorentz forces of ions and electrons in magnetic field are shown in Fig. 3. It does not change the magnitude of the charged particles’ velocity but the direction of motion. In other words, the particles cannot gain kinetic energy from Lorentz force. The increasing of kinetic energy of a charged particle is contributed by the energy of electric field. Because the ions are much heavier than the electrons, the ions contribute substantially to the thrust. The ions are canted toward the cathode for the ion is positive charged by the influence of electric field. This is the reason why
2
4 3
6
5
THRUST
ANODE
Fig. 4. Motion directions of ions and electrons.
the cathode contamination looks more serious than that of the anode. The relation between several geometric configurations of electrodes and the acceleration is discussed below. Electrode length: After the electrothermal acceleration, the motion directions of ions and electrons are shown in Fig. 4. Because the Lorentz force is perpendicular to the motion direction of particle, the direction is bent to a circle with a radius named Larmor radius, which is given by R=
mv , qB
(7)
where m is the mass of the particle. The particle velocity is increased as a result of the electric field and its direction is changed by the self-induced magnetic field. The magnitudes of the electric field and the selfinduced magnetic field always change with time hence varies Larmor radius. When the Larmor radius is smaller than the length of the electrode, the motion direction of the particle reverses and more ions impact the cathode. The mass loss weakens the thrust. Generally, the longer the acceleration time of particles within electric field, the more the kinetic energy of particles will get. If the electrodes are too short, there is no enough time for particles to reach a high velocity. This leads to a low accelerating effect. That is to say, the electrode length
408
H. Dali et al. / Acta Astronautica 62 (2008) 404 – 409
350 30mm 40mm 50mm
300
Thrust/µN
250
200
150
100
50
2
4
6
8
10
12
14
16
18
20
Discharge energy/J Fig. 5. Relation curves between thrust and discharge energy (electrode gap = 30, 40, 50 mm).
influences the PPT performance greatly. An optimized result is achieved by changing the value of the accelerated distance and the Larmor radius. Electrode gap: An increase in the electrode gap induces a rise in the exposed area of propellant. Correspondingly, the quantity of the ablated particles is increased. When the chamber volume keeps invariable, the increase of ablated particles quantity leads to an elevated pressure. Then, the pressure enhancement causes the increase of gas-expanding force. But the chamber volume also extends when the electrode gap becomes larger. The reduced chamber pressure resulting from extended volume has strong influence for the gas-expanding force reduction. Therefore, the electrode gap is a balance of the ablated particles quantity and the chamber volume. Works by Palumbo and Guman shows that the electrode gap has an optimal point. Once the gap deviates from this point, the efficiency decreases quickly [9]. Electrode width: Increasing the electrode width leads to the increase of the exposed surface area of propellant and the chamber volume. The elevated exposed area increases the quantity of particles when discharge occurs. This makes the chamber pressure increase if the chamber volume is constant. But the increasing of the chamber volume results in the lower pressure correspondingly. The electrode width also has an optimized value for acceleration. It is similar to electrode gap.
Discharge energy: The change of discharge energies is also evaluated. When the discharge energy augments, the discharge current, the magnitudes of electric field and magnetic field will also increase. Then it is possible to achieve a better performance of electromagnetic acceleration. The data showed that the thrust increased almost linearly over the range of discharge energies tested in our experiments. It is shown in Fig. 5. 4. Conclusions A new understanding about plasma acceleration in PPT is presented. The process is described in detail, which includes two stages: electrothermal acceleration and electromagnetic acceleration. Near the propellant surface, electrothermal acceleration is primary and provides initialized ions velocity for electromagnetic acceleration. Electromagnetic acceleration is the secondary acceleration for ions and electrons. In electrothermal acceleration stage, the plasma pressure should be enhanced to ameliorate the acceleration. Some measures such as improving temperature and reducing the volume of acceleration channel can be taken to improve the gasexpanding force. In the second stage, that is electromagnetic acceleration stage, the discharge current should be improved to get better performance. The electrode gap and electrode length also have an optimized value for the best overall performance. The methods to improve
H. Dali et al. / Acta Astronautica 62 (2008) 404 – 409
particle accelerating factors in PPT should be carefully chosen according to the characteristics of corresponding acceleration stage.
[5]
References [6] [1] G.G. Spanjers, J.B. Malak, R.J. Leiweke, R.A. Spores, The effect of propellant temperature on efficiency in the pulsed plasma thruster, in: 3rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Seattle, WA, July 6–9, 1997. [2] R.J. Cassady, et al., Pulsed plasma thruster systems for spacecraft attitude control, in: Proceedings of the 10th AIAA/USU Conference on Small Satellites, 1996. [3] G. Spanjers, Propellant inefficiencies in pulsed plasma thrusters, in: 6th Aerospace Sciences Meeting, January 22–24, AIAA 6885, New York, USA, 1968. [4] F. Rysanek, R.L. Burton, Effects of geometry and energy on a coaxial teflon pulsed plasma thruster, in: 36th AIAA/ASME/
[7] [8]
[9]
409
SAE/ASEE Joint Propulsion Conference, Hunstville, AL, July 17–19, 2000. W.A. Hoskins, R.J. Cassady, Development of a micro pulsed plasma thruster for the dawgstar nanosatellite, in: 36th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Hunstville, AL, July 17–19, 2000. L.A. Arrington, C.M. Marrese, J.J. Blandino, Pulsed plasma thruster plasma study: symmetry and impact on spacecraft surfaces, in: 36th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Hunstville, AL, July 17–19, 2000. G.A. Popov, N.N. Antropov, Ablative PPT. New quality new perspectives, ACTA ASTRONAUTICA 59 (2006) 174–180. G.G. Spanjers, K.A. McFall, F.S. Gulczinski III, R.A. Spores, Investigation of propellant inefficiencies in a pulsed plasma thruster, in: 32rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Lake Buena Vista, FL, July 1–3, 1996. W.J. Guman, P.E. Peko, Solid propellant pulsed plasma microthruster studies, Journal of Spacecraft and Rockets 6 (6) (1968) 732–733.
Operation analysis of pulsed plasma thruster Hou Dali∗ , Zhao Wansheng, Kang Xiaoming School of Mechanical Engineering, ShangHai Jiao Tong University, No. 800, Dongchuan Rd., ShangHai 200030, China Received 3 January 2007; accepted 8 January 2008 Available online 14 February 2008
Abstract Pulsed plasma thruster (PPT) is an attractive micro-thruster for many flight missions. Compared to other electric propulsion systems, PPT is more compact, lightweight and robust while lower in thrust efficiency. It is very difficult to solve this problem because of lacking of theoretically thorough understanding of the energy transformation. In this paper, an attempt was made to explain the process from a different viewpoint where the acceleration is divided into two stages based on the dominative status. At the beginning of discharge, the electrothermal acceleration is primarily near the propellant surface. In the second stage, ions and electrons are accelerated by the electromagnetic field induced by the discharge between the electrodes. Electromagnetic acceleration contributes substantially to the thrust. Some measures should be taken to ameliorate the electrothermal acceleration at the first stage and enhance the electromagnetic acceleration at the second stage. For the purpose of improving thrust efficiency, the relations between the acceleration and electrode gap, electrode width, discharge energy have been discussed. Some methods by modifying design parameters are presented to enhance the accelerating effect. © 2008 Elsevier Ltd. All rights reserved. Keywords: Pulsed plasma thruster; Thrust; Specific impulse; Thrust efficiency
1. Introduction Pulsed plasma thruster (PPT) is an electric propulsion device using electric power to ionize and electromagnetically accelerate plasma to high exhaust velocity. PPT has a broad prospect on small satellites. It has many features which make the PPT more attractive than traditional propulsion. Firstly, the PPT offers a high specific impulse compared to other micro-thrusters. Typically its specific impulse ranges from 800 to 1200 s. Secondly, PPT is small, robust, compact and low mass. As the spring is the only removable part, the structure of PPT is of higher reliability than other systems. Using Teflon as its propellant allows significant reductions ∗ Corresponding author. Tel./fax: +86 21 6293 4959.
E-mail address: [email protected] (H. Dali). 0094-5765/$ - see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.actaastro.2008.01.004
in mass and volume of the thruster by eliminating the propellant tankage and valves [1]. Thirdly, PPT operates at low power level and its pulsed nature permits operation over a relatively broad power range without loss of performance. Power supply is generally below 100 W. The low power level is fit for small satellites and can regulate the power supply by changing the discharge frequency. For example, when changing the discharge frequency from 1 to 0.01 Hz, the power level can be reduced to 1% of its original power level. Thus, the mass of power supply is reduced, thereby reducing the launching cost of the satellites. Lastly, the impulse bit is low; it ranges from tens to hundreds of N s. PPT can provide both impulse force and continued force. Continued force can be regulated easily by varying the discharge frequency. The PPT is extremely flexible and can easily be customized to meet propulsion
H. Dali et al. / Acta Astronautica 62 (2008) 404 – 409
requirements for a wide variety of missions. For this reason, it has been used in attitude control, orbit distracting and drag compensating, etc. For example, in attitude control system, PPT provides stabilization instead of reaction wheels only needing lower cost, lower mass and power requirements [2]. However, the overall efficiency of PPT is very low, that limits its application in some conditions. The PPT for the LES8/9 has a thrust efficiency of 7% and the PPT of EO-1 is about 8%. The efficiency of PPT reported in recent years is rarely exceeds 10%. The reasons are listed as follows. Firstly, PPT is inefficient when transferring stored capacitor energy into acceleration of the ionized propellant. Secondly, mass utilization efficiency in PPT is low (< 50%) because of two performance robbing processes—late-time vaporization [3] and macro-particles ejection. Many propellant particles are wasted in the form of propellant vapor and large chunks. The thrusters have very low efficiency due to a combination of poor energy coupling into the propellant, late-time ablation, and inefficient acceleration. The study of plasma accelerations is very important to solve the lower thrust efficiency. In this paper, the process from discharge to thrust generation is described and a new idea to understand the acceleration theory is provided. It is very helpful to design a high efficient PPT. 2. Fundamentals The PPT systems are completely self-contained propulsion modules. Generally, it includes a power source, a power processing unit (PPU), an energy storage unit, and the thruster itself. Solar cells are generally used as power sources, since the thruster operates at a low power level. The main functions of the PPU are to provide the charging voltage for the energy storage unit and to provide the command and telemetry functions required to operate the PPT. The energy storage unit provides high-current pulses through the thruster to perform work. Capacitor is often used as an energy storage unit. Thruster typically consists of two electrodes, the propellant, a negater spring and a spark plug. The configuration of PPT is illustrated in Fig. 1. At the beginning of PPT operation, the capacitor is charged to the desired voltage. The spark plug is ignited to trigger the discharge. The energy stored in the capacitor powers a high-current duration plasma discharge and produces an electromagnetic field. Then the molecules of propellant are ionized. Due to the actions of a J × B electromagnetic Lorentz force and gas-expanding force,
405 Spark Plug Cathode
Propellant
Plasma
Anode Capacitor
+
PPU
-
Fig. 1. Basic schematic of PPT.
the plasma is accelerated to high exhaust velocities and thrust is generated. 3. Discussion For the purpose of improving the efficiency of PPT, the related theory is studied to increase mass utilization efficiency and power efficiency. The crucial difficulty in PPT modeling is lacking of theoretically thorough understanding of the process of energy transfer from discharge to solid propellants and mass ablation. The electromagnetic and thermal phenomena involved in propellants acceleration are very complicated. There is still no physical model to accurately predict the behavior of the thruster. Generally, there are two types of acceleration mechanisms employed in PPT which are electromagnetic acceleration and electrothermal acceleration [4]. In the electrothermal acceleration stage, the thrust is produced by gas expansion which is caused by discharge. In the electromagnetic acceleration stage, a thrust is produced by accelerating ionized particles in the electric field and the self-induced magnetic field. The thrust of PPT is defined as [5] T = TEM + TET
(1)
with TEM the electromagnetic force and TET the thrust contributed by the gas dynamic expansion, i.e. the electrothermal force. TEM is expressed by 0 h t 2 i dt, (2) TEM = f 2 w 0
406
H. Dali et al. / Acta Astronautica 62 (2008) 404 – 409
where f is the pulse frequency, i is the total current calculated by RLC circuit analysis, 0 is the magnetic permeability, h is the gap between the electrodes, w is the width of the electrodes and l is the length of the electrodes. TET is given by 1/2 8( − 1) TET = f 2 ·m·E , (3) ( + 1) where m is the mass loss per impulse and is a constant decided by the propellant materials. For Teflon, = 1.3. E is the total energy of PPT discharge. To achieve the best PPT performance, it is necessary to improve the electromagnetic force and the gas-expanding force. Thus, it is very important to understand the acceleration. At the beginning of discharge, the spark plug is ignited by a high voltage. Some electrons are produced and impact the surface of the propellant with a high velocity. The particles include ions, electrons and neutral particles escaping from propellant. With the effect of strong electric field between cathode and anode, these ions are accelerated and keep on impacting the propellant. Plasma comes into being between the electrodes for the reason of the frequent collisions between particles (including electrons, ions and neutral particles) and propellant. The compositions of this plume are carbon, fluorine, and a variety of fluorocarbons including CF3 , CF2 , and CF [6]. It is difficult to explain the complicated electromagnetic and thermal phenomena involved in propellants acceleration. Firstly, the electrothermal acceleration occurs near the propellant surface where the discharge happens. Once the plasma forms, the electrodes become conductive and main discharge occurs. The discharge ablates the propellant and produces more particles, which makes the pressure near the propellant surface increases greatly. A part of the power transfers into heat and increases the temperature of plasma. This makes the pressure of PPT chamber increase rapidly. Particles are then accelerated by the high pressure in the chamber of the PPT. This is the first stage of acceleration, i.e. electrothermal acceleration. This acceleration is mainly induced by thermal energy generated by discharge. In this stage, particles have not entered into the electric field and there is no electromagnetic acceleration. The density of the plasma is low and can be regarded as rarefied plasma. The relation of the pressure, volume and temperature for rarefied plasma is described by Clapeyron equation P V = nR 0 T ,
(4)
where P represents the pressure of plasma, V is the volume of PPT chamber, T is the temperature of plasma, n is the quantity of mole and R0 is a constant expressed by R0 = 8.314 J/mol K.
(5)
Late-time vaporization happens in this stage. Even though in electrothermal PPT which mostly thrust comes from electrothermal acceleration, up to 70% of propellant can reach acceleration channel of the thruster after the main discharge finish or at the moment of considerable discharge current drop [7]. To make more particles reach the acceleration channel, the pressure of plasma should be increased. From Eq. (4), increasing the temperature of plasma is an effective way. The high energy of discharge is used to increase the thermal energy. The temperature rises and the thrust correspondingly increases. The temperature should not be too high after discharge otherwise it will cause more particles escaping from propellant which makes low mass utilization efficiency. Macro-particles are believed to be ejected from the propellant and electrode surfaces as a result of local overheating thereby leads to low propellant efficiency [8]. This part of propellant loss produces a negligible thrust because of the low particle velocity (< 3 km/s). The other way round, keeping propellant temperature low after discharge will realize a significant savings in propellant mass. Improving the quantity of particles i.e. n in Eq. (4) is an efficient method to increase the thrust. Enlarging exposed area of the propellant is often adopted to improve the thrust. Decreasing the chamber volume near the propellant surface is another method. This is the reason why many electrothermal PPTs have very small volume at the end of the chamber. In the second stage, electrothermal accelerated particles enter into the electric field. The gas-expanding effect becomes weaker when particles are far away from the surface of the propellant. The neutral particles are not affected by electric field and cannot be accelerated. Previous researches have concluded that as little as 10% of the consumed propellant is converted to plasma and efficiently accelerated to a high velocity by electromagnetic forces [1]. It is about 90% of the propellant, i.e. neutral particles can not get an electromagnetic acceleration. Thus, the existence of neutral particles is an important reason for the low efficiency of PPT. In this stage, the charged particles achieve high velocity. Although those particles have less mass than neutral particles, they contribute much more to the momentums. Therefore, the electromagnetic acceleration is very important for the PPT performance. Neutral particles take
H. Dali et al. / Acta Astronautica 62 (2008) 404 – 409
407
SPARK PLUG CATHODE
B
F PROPELLANT
PLASMA
B
THRUST
V
V
F
ANODE
Fig. 3. Lorentz forces of ions and electrons in magnetic field.
SPARK PLUG ELECTROTHERMAL ACCELERATION
ELECTROMAGNETIC ACCELERATION
CATHODE 1
Fig. 2. Schematic of acceleration stage. PROPELLANT
most of mass but get no electromagnetic acceleration because of lacking electric charge. This poor mass utilization represents a main factor to the low efficiency of PPT. Nowadays, studies on improving thrust efficiency area mainly focused on ameliorating the electromagnetic acceleration and decreasing the amount of neutral particles. Fig. 2 is the illustration of the acceleration process. In order to analyze the electromagnetic acceleration, the behavior of charged particles in magnetic field should be studied. The Lorentz force law is described as f = qE + qv × B.
(6)
It gives the definition of the force acting on a charge q moving with velocity v in an electric field E and a magnetic field B. The magnitude of the magnetic force exerts on a moving unit charged particle is the product of the particle’s charge, its velocity and the magnetic flux density. The initial charged particle velocity is a result of the electrothermal acceleration. The Lorentz force is perpendicular to both the velocity v of the charge q and the magnetic field B. The magnetic force on a stationary charge or a charge moving in parallel to the magnetic field is zero. The Lorentz forces of ions and electrons in magnetic field are shown in Fig. 3. It does not change the magnitude of the charged particles’ velocity but the direction of motion. In other words, the particles cannot gain kinetic energy from Lorentz force. The increasing of kinetic energy of a charged particle is contributed by the energy of electric field. Because the ions are much heavier than the electrons, the ions contribute substantially to the thrust. The ions are canted toward the cathode for the ion is positive charged by the influence of electric field. This is the reason why
2
4 3
6
5
THRUST
ANODE
Fig. 4. Motion directions of ions and electrons.
the cathode contamination looks more serious than that of the anode. The relation between several geometric configurations of electrodes and the acceleration is discussed below. Electrode length: After the electrothermal acceleration, the motion directions of ions and electrons are shown in Fig. 4. Because the Lorentz force is perpendicular to the motion direction of particle, the direction is bent to a circle with a radius named Larmor radius, which is given by R=
mv , qB
(7)
where m is the mass of the particle. The particle velocity is increased as a result of the electric field and its direction is changed by the self-induced magnetic field. The magnitudes of the electric field and the selfinduced magnetic field always change with time hence varies Larmor radius. When the Larmor radius is smaller than the length of the electrode, the motion direction of the particle reverses and more ions impact the cathode. The mass loss weakens the thrust. Generally, the longer the acceleration time of particles within electric field, the more the kinetic energy of particles will get. If the electrodes are too short, there is no enough time for particles to reach a high velocity. This leads to a low accelerating effect. That is to say, the electrode length
408
H. Dali et al. / Acta Astronautica 62 (2008) 404 – 409
350 30mm 40mm 50mm
300
Thrust/µN
250
200
150
100
50
2
4
6
8
10
12
14
16
18
20
Discharge energy/J Fig. 5. Relation curves between thrust and discharge energy (electrode gap = 30, 40, 50 mm).
influences the PPT performance greatly. An optimized result is achieved by changing the value of the accelerated distance and the Larmor radius. Electrode gap: An increase in the electrode gap induces a rise in the exposed area of propellant. Correspondingly, the quantity of the ablated particles is increased. When the chamber volume keeps invariable, the increase of ablated particles quantity leads to an elevated pressure. Then, the pressure enhancement causes the increase of gas-expanding force. But the chamber volume also extends when the electrode gap becomes larger. The reduced chamber pressure resulting from extended volume has strong influence for the gas-expanding force reduction. Therefore, the electrode gap is a balance of the ablated particles quantity and the chamber volume. Works by Palumbo and Guman shows that the electrode gap has an optimal point. Once the gap deviates from this point, the efficiency decreases quickly [9]. Electrode width: Increasing the electrode width leads to the increase of the exposed surface area of propellant and the chamber volume. The elevated exposed area increases the quantity of particles when discharge occurs. This makes the chamber pressure increase if the chamber volume is constant. But the increasing of the chamber volume results in the lower pressure correspondingly. The electrode width also has an optimized value for acceleration. It is similar to electrode gap.
Discharge energy: The change of discharge energies is also evaluated. When the discharge energy augments, the discharge current, the magnitudes of electric field and magnetic field will also increase. Then it is possible to achieve a better performance of electromagnetic acceleration. The data showed that the thrust increased almost linearly over the range of discharge energies tested in our experiments. It is shown in Fig. 5. 4. Conclusions A new understanding about plasma acceleration in PPT is presented. The process is described in detail, which includes two stages: electrothermal acceleration and electromagnetic acceleration. Near the propellant surface, electrothermal acceleration is primary and provides initialized ions velocity for electromagnetic acceleration. Electromagnetic acceleration is the secondary acceleration for ions and electrons. In electrothermal acceleration stage, the plasma pressure should be enhanced to ameliorate the acceleration. Some measures such as improving temperature and reducing the volume of acceleration channel can be taken to improve the gasexpanding force. In the second stage, that is electromagnetic acceleration stage, the discharge current should be improved to get better performance. The electrode gap and electrode length also have an optimized value for the best overall performance. The methods to improve
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particle accelerating factors in PPT should be carefully chosen according to the characteristics of corresponding acceleration stage.
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