AIAA-2002-3803 Acceleration of Pulsed Electromagnetic Plasmas Y. C. Francis Thio _ Jason T. Cassibry 2 T. E. Markusic _ (1) George C. Marshall Spaceflight Center (2) University of Alabama in Huntsville. AIAA/ASME/SAE/ASEE Joint Propulsion 38 th Conference & Exhibit 7-10 July 2002. Indianapolis, Indiana For permission to _'¢_1))o'r to veple_i._h, l'o, la_:!lhe _Anwrk'an ln_lilul¢ =&Acr_ naut,..'_ and A_tr_m;.utk_. i_l)l Ak.x.ntler Ik'll Drive, Suit_e5(N), Rcston, %%.,];ill 91-4344. AIAA-2002-2194 Pulsed Electromagnetic Acceleration of Plasmas Y. ( Francis Thio, Jason T. Cassibry l,Thomas E. Markusic NASA Marshall Space Flight Center Abstract region between the electrodes. This magnetic field acts on the plasma current to produce the electromagnetic j x A major shift in paradigm in driving pulsed plasma B (Lorentz) force on the plasma, accelerating the plasma thruster is necessary if the original goal of down the tube. The 'Holy Grail' of PPT research has accelerating a plasma shett efficiently to high been to find a way to use the intrinsically highly velocities as a plasma "slug" is to be realized. Firstly, efficient j x B (Lorentz) force to accelerate a plasma the plasma interior needs to be highly collisional so "slug" cleanly with a precise current pulse, leaving that it can be dammed by the plasma edge layer nothing inside the thruster after the current pulse with (upstream) adjacent to the driving 'vacuum' the plasma slug exiting the barrel with an uniform magnetic field. Secondly, the plasma edge layer needs velocity. This has simply not been achieved to date. In a to be strongly magnetized so that its Hall parameter real PPT, the plasma is anything but a "slug" and is of the order of unity in this region to ensure displays a wide range of complex behavior. In fact, one excellent coupling of the Lorentz force to the plasma. may say that there is a tendency for the PPT to behave Thirdly, to prevent and/or suppress the occurrence of more like a quasi-steady-state MPD thruster. In that secondary arcs or restrike behind the plasma, the mode one may say that it has the worst of both worlds. region behind the plasma needs to be collisionless Considerable amount of effort has been expended in and extremely magnetized with sufficiently large Hall understanding the complexities of the plasma behavior parameter. This places a vacuum requirement on the in PPT. In this paper, we take the opposite approach. We bore conditions prior to the shot. These requirements ask the question, "what plasma conditions must we are quantified in the paper and lead to the provide mother nature in the PPT so that the plasma will introduction of three ne_ design parameters behave in an ideal manner?" Preliminary considerations corresponding to these three plasma requirements. on the engineering implementation of the proposed The first parameter, labeled in the paper as 71, "plasma agenda" are discussed in this paper as well as in pertains to the permissible ratio of the diffusive the companion paper [1]. excursion of the plasma during the course of the acceleration to the plasma longitudinal dimension. 2 Performance Losses in PPT The second parameter is the required Hall parameter of the edge plasma region, and the third parameter is The performance of past PPT's in flight or in the required Hall parameter of the region behind the laboratories have been reviewed recently by several plasma. Experimental research is required to authors [2-4]. The principal performance losses and quantify the values of these design parameters. Based engineering issues may be summarized as follows: upon fundamental theory of the transport processes 1. Low propellant utilization efficiency. This is in plasma, some theoretical gttidance on the choice of perhaps the most important performance loss and these parameters are provided to help designing the relates to the fact that even though some plasma necessary experiments to acquire these data. pieces may be launched out of the thruster at a velocity v, the steady-state specific impulse 1 Introduction achieved is considerably lower than vlg. Several mechanisms contribute to this. Some are of an A coaxial pulsed plasma thruster (PPT) is a plasma engineering nature relating to the feeding of accelerator consisting of a pa, of coaxial cylindrical propellant and in principle they may be overcome electrodes. Current from a pulsed power supply, with suitable engineering ingenuity[I]. The typically a capacitor bank, enters at one of the inherently more challenging issues are related to electrodes, crosses the gap between the electrodes undesirable plasma behavior. For example, large through a plasma, and returns to the capacitor bank via amount of ablation of the breech was observed the other electrode. The current following in the during the late phase of the discharge[4]. Due to electrodes generates an azimuthal magnetic field in the poor coupling of the Lorentz force to this cold iUniversity of Alabama, Hunts_ ille, USA. AIAA-2002-2194 material, it acquires very lit',le velocity. Though this 3 A High-Energy Pulsed Plasma ablation could be caused by direct radiation from Thruster the main plasma, more lil..cly than not, the main source of this late-time _blation is due to the To make our discussion concrete, we will introduce our thermal transport from sec_,ndary arcs that may be discussion in the context of designing a pulsed formed by the following pr(._:csses: electromagnetic plasma accelerator as a driver for an • Arc restrike at the breech, or at any parts of the experiment in magnetized target fusion (MTF) [5]. For a accelerator between l]-.c breech and the main near-term physics exploratory experiment to study the plasma. formation of a plasma shell for MTF, a pulsed plasma • Instabilities of the man plasma leading to its accelerator is required to launch pulsed plasma jets with fragmentation. a mass approximately 1 mg to more than 200 km/s [6]. Any electrode erosion ;Jssociated with these Twelve of these plasma jets are used simultaneously to processes would further add to the parasitic implode a target placed at about 0.5 m away. For this propellant mass. application, extremely low temporal and spatial jitters of . Low pulsed-power driver efficiency. This is caused the launch (less than 100 ns and 1 cm respectively). by the usually large mismatch in the impedance of Good focusing and collimation properties of the plasma the pulsed-power driver (th,: capacitor, the switches, jet are additional requirements that are well beyond the the transmission lines) anti the PPT, especially in usual requirements for propulsion applications. experimental laboratory t'PT's. PPT's are low- inductance devices, whereas laboratory pulsed The baseline concept for this purpose consists of a power supplies typically have large parasitic shaped coaxial plasma accelerator as shown in Figure 1. inductances. Significant ann,_unt of electrical energy The plasma design in support of the concept is the main remains in the external circait after the main plasma objective of the present paper and will be developed in has left the accelerator _n typical experimental the next two sections below. In this section, we will devices. This residual energy is often wasted in describe the engineering concepts and schemata that producing undesirable discharges and entropy inside serve to implement the plasma design. the accelerator. Electrode erosion. 3. The accelerator consists of a pair of coaxial electrodes. 4. Reliability. Fatigue in the _arious components is an The outer electrode has a diameter of 20 cm and is about important life-time issue for the repetitive operation 0.75 m long. The inner electrode has a diameter of 10 of a pulsed plasma thruster system for any practical cm, and about 0.5 m long. Both electrodes have a operation. External switches are particularly gradual conical taper and an electromagnetic focusing vulnerable to this issue. section (much like a plasma focus device) to inducc a Outer conductor Plasma feed Figure 1. The baseline concept for PEPA-I. ] & Current trigatrons flow Refractory Insulator Electromagnetic Plasma (BN, or focusing flow Si3N4) Inner conductor -lmg Nearly collimated flow - 200 km/s resulting from balancing of the focusing flow against Contoured gun wall fiw thernml expansion nlechanical focusing radially AIAA-2002-2194 _V _---> -- r_ .... ..*... \} Figure 2. The three regions of the plasma: (1) The plasma edge region, (2) the plasma interior, (3) the plasma front. The curves denoted as B and j are the profiles of the magnetic field and current density. 4 The Plasma Physics Prescription inward velocity at the muzzle exit to compensate for the The principal 'malfunction' of the plasma dynamics in thermal expansion during the flight of the plasma jet to typical PPT's is the failure of the magnetic field to the target. This is not normall) required for propulsion confine the current distribution to a finite region in the application. The acceleration chamber is thoroughly accelerator. As a result secondary arcs are formed, either flushed with helium and evacu_ued (no gas pre-fill) to a in the form of a restrike or a fragmentation of the main vacuum to be prescribed in ,Section 4. The required plasma due to plasma instabilities. As the velocity of the plasma mass (all of the 1 m_t is introduced into the current "sheet" increases, the motional back emf (= I acceleration chambei by a set of (6 to 12) extremely L'v) also increases. This voltage is applied at the breech low-jitter (< 10 ns) pulsed ldasma feeds (injectors) to the accelerator. The bore of the accelerator is an arranged annularly near the breech. The plasma feed extremely active environment electrically. It is produces the plasma either by w_porizing a liquid film or permeated by a relative abundance of charged particles ablating appropriate solid line_ or fiber using a pulsed and neutrals left behind by the moving plasma, or from discharge. The plasma feed launches the plasma in the the products of ablation, or by the photoionization of the form of a plasma 'fan' (or 'plume') radially toward the neutrals resulting from any gas in the bore before the axis of inner electrode. The plasma fans join to form an pulse. If there is any significant amount of neutral dense plasma sheet that closes the external circuit and particles present behind the plasma, Townsend brings on the main current pulse to accelerate the plasma avalanche could occur producing restrike. The presence sheet down the accelerator. of neutrals behind the plasma is a principal cause for the formation of secondary arcs. The plasma feeds inject the plasmas transversely to the accelerator and are placed at some distance from the The ratio (t3) of the plasma (thermal) pressure (nkT) to breech to allow some room 1,_r the initial plasma to the magnetic pressure (B2/2,u) is an important parameter expand backward before the "c_Jrrect" plasma dynamics in determining the quality of confinement of a plasma by is fully established according 1, the prescription of the a magnetic field. The intrinsic difficulty in accelerating a next section. It is crucial that this plasma is not allowed plasma by the self field of the driving current lies in the to be in contact with the breech so that thermal fact that the plasma fl varies from 0 to _ over the conduction to the breech insul,qlor can be suppressed by thickness of the plasma current sheet. Thus, while the the "vacuum" magnetic field. Additionally, refractory upstream (rear) part of the plasma may be strongly insulators are used for the breech to withstand any magnetized so that it can be 'dammed' by the magnetic radiative transport from the plasma. Candidate insulators field, the downstream (frontal) part of the plasma is at are boron nitride or silicon nitriJe. most weakly magnetized so that the only way to dam this part of the plasma is by collisions between the plasma particles. AIAA-2002-2194 The difficulty is compounded it the plasma is not fully ionized. We will at the outset demand that our plasma be ,,,_> Jt'z lnA)L(r'L.)'i_l nearly fully ionized by dJiving the plasma to (4.3) temperatures much higher than is usual in past PPTs. where k is the Boltzmann's constant, m, the electron This is done by driving the pla.',ma with current density mass, T_ the electron temperature. SI units are used level which are orders of magnitude higher than is usual, throughout this paper, including the temperature being and thus obtaining plasma teml,cratures of several eV's given in degrees Kelvin. In A is the usual Coulomb (say, greater than 4 eV). logarithm. Using the design of PEPA-1 as an example, with tp = 5 Its, and the reasonable choices of 0.1 for _'1 Our plasma strategy consists of firstly demanding the and the plasma dimension Lt, as half the interelectrode plasma interior to be highly dense with a high degree of gap = 0.5(r2 - rl) = 2.54 cm, an electron temperature of 4 collisionality to ensure that th_ plasma behaves like a eV, and assuming Z = 1, the above expression gives n_= fluid. Secondly, the plasma edge region (upstream) in 2.8 x 1023per m3,about two orders of magnitude higher contact with the 'vacuum' magi/eric field to be strong!y_! than what is typical in past PPT experiments. With the magnetized to ensure magnetic confinement. Thirdly we above prescription of the main plasma, the plasma has a require that the region behind the plasma to be strong[y_l mass of about 0.98 mg, as required for our experimental magnetized and collisionless to the extent that the accelerator PEPA- 1. magnetic field provides electric.d insulation like the way an ordinary insulator is used it, preventing arcing. This For the plasma edge region to be strongly magnetized, last requirement puts an upper bound on the gas density the electron Larmor radius should be smaller than the in the accelerator before the pulse, i.e. the vacuum electron-ion collision mean free path. This is the same as requirement for the acceleratin:_, chamber. Fourthly, we will seek to avoid any possible complications from any requiring the Hall parameter (o_x_i) to be greater than 1. To indicate the trend and the order of magnitudes of the significant space charge effects by demanding quasi- magnetic field required, a Hall parameter of at least 2 neutrality. We will now quantily the underlined terms. leads to a magnetic field of at least 3.3 T. Taking this to be the magnetic field at a point midway between the For collisionality in the plasma interior, we require that inner and outer electrodes, the driving current required random walk of the particles due to collisions will not to produce this magnetic field is 1.26 MA. Again, past travel more than a prescribed percentage (denoted as "h) PPT experiment uses magnetic field typically of the of the plasma dimension (Lp). "Ihe distance traveled by a order of 0.1 - 0.5 T. We note that, current conduction in random walk in N,. collisions it go = _/N-[-_2where 3.is a strongly magnetized plasma can only occur across the the mean free path between collisions. For a fully magnetic field in the presence of a Hall electric field to ionized plasma the electron-io, mean free path is the provide the necessary E x B drift. Thus, the Hall current relevant collision length. Let the desired acceleration is an essential part for the proper operation of a pulsed time be tp.Our first collisionaliiy requirement leads to plasma thruster. We also note that the choice of a Hall parameter of the order of unity will lead to some canting =(v,",LI:7< of the current sheet. But the canting of the current sheet (4.1) by itself does not necessarily degrade the performance of the accelerator as the forward component of the net Lorentz force on the plasma is independent of the where Vte is the thermal .,peed of the electrons current distribution within the plasma so long as the current distribution is steady with respect to the current. v_ Canting of the current sheet, however, could lead to (= k_T_/, is the electron ion collision frequency Vm, ) higher, unbalanced plasma pressure and density against given in SI units as [7], the electrodes resulting in higher skin friction and other plasma boundary effects. vei= bZ2nTi31I-n--A------b-"-="y.__, 3__2!e4-3/2 u2 - 3.6332 x10.6 Immediately behind the plasma, even stronger • 1Z7¢ EI K me magnetization is required, so that any electrically (4.2) charged particles that might be present in this region will The above expressions yield for the ion density required be confined to move in circles about the magnetic field to be, lines with radii considerably smaller than the collision mean free path and the bore dimensions. Collisions will allow the particles to diffuse across the field lines with the potential for producing the very dangerous 4 AIAA-2002-2194 Townsend avalanche. Because ,,f the proximity to the the third term on the right hand side of the expression. plasma, any charged particles p_-esent in this region will This Hall electric field produces a E x B drift in the be assumed to have a kinetic te_perature similar to that opposite direction to the original current, and reduces the of the plasma. net current flow. To see this, the above expression can be inverted as was done by Braginskii to give the current In the region behind the plasma, the strong density in terms of the electric field as, magnetization requirement apphcs to the ions as well as the electrons whose Larmor r:_dius are much smaller • ' o-± LFE"±+ _, _',e, xE'-JI (4.6) than the ions for the same kinetic temperature. This : o-,,E* ,,+ ,,,)' requires that the ion Larmor radius to be substantially smaller than the smallest collision mean free path, i.e. the electron-ion mean free path. This is equivalent to where eB is a unit vector in the direction of the magnetic field, o4 is the electron cyclotron frequency, and _ is requiring that the ion Hall parameter (_%_) for this 'vacuum' region to be extremely large. The difficulty to the electron-ion collision time. a__',,is known as the Hall proceed with the design here is the lack of appropriate parameter. It is seen from the above expression that with experimental data that could help us with making a sufficiently large value of the Hall parameter, the suitable design choices for this important parameter. current density across the field lines can be significantly This an obvious area for future experimental research. suppressed. The above expression may also be used as a basis to explain the canting of the current sheet in Some theoretical guidance may be provided by a review traditional PPT's. of the transport processes in a plasma. According to Braginskii [8], in a single-fluid magnetohydrodynamic From the above expression, it follows that for large description of a plasma, the 'elfective' electric field E' value of the Hall parameter, the current density is in the presence of a magnetic field B at a position in a reduced by a factor in inverse proportion to the Hall plasma is related to the current dcnsity j flowing at that parameter. Thus by choosing the Hall parameter suitably position by, large, current flowing in the region behind the plasma can be suitably suppressed. To bootstrap the • " jxB experimental develo6Pment of PEPA-1, we will use a E'= JIt+JL I (4.4) value of at least 10 for the design of the experiment. 0"11 Cri n e This design choice is far from being an overkill because of the large electrode surface area behind the plasma where, compared to the conduction area for the plasma. To ensure that any current flowing in this region will be small compared to the main plasma current, a large E'=E+vxB+_I (Vp,-Rr). (4.5) value of this order would indeed be required for the Hall ne parameter. Using this value, the particle density in the region behind the plasma needs to be maintained at In the above expressions, the subscripts 11and_L indicate below 4 × 1019 per m 3. This is a vacuum prescription for the components of the vector _r the physical property the accelerating chamber prior to the shot. Helium has parallel and perpendicular to th:• magnetic field, o-is the the property of being difficult to break down. Using plasma electrical conductivity, ,,_is the electron density, helium to flush out the accelerator before firing, a e is the electronic charge, p_ is the electron pressure, and vacuum of below 1milli-torr is required. Rr is the thermal force on the electrons due to electron temperature gradients. To check for the plausibility of our assumption for the plasma temperature, an estimate for the plasma In Expression (4.4), the sec_,nd term involving the temperature may be obtained by balancing the ohmic perpendicular resistivity (l/crz) is a result of heating in the plasma against the radiation losses. momentum transport across lhe field lines due to Expression (4.6) may be used conveniently to provide an electron-ion collisions. The perpendicular resistivity is at estimate for the ohmic heating in terms of the effective electric field (in the frame of the moving plasma) as most twice the parallel resisti,,ity (1/o'ii). Looking at follows: this term alone, it might seem that it is not possible to use magnetic field to suppress the flow of current behind the plasma. This is erroneous because the flow of such a Ql_= j'J'_J "E'd3r, V- plasma volume (4.7) current behind the plasma across the magnetic field lines = n'(r_ - rl2)wj-E ' will necessarily produce the Hall electric field given by AIAA-2002-2194 C4 where, the plasma is modeled as a lumped mass dement accelerated by the Lorentz force. (')"2_ P2 j'E' = O"11E2if+ 1 (1+(_r.,)2) E± FL =--L'I 2 (4.8) 2 e2nVi 1 cr.=_, r,,=-- where 1 is the current through the plasma and L' is the m e Vei inductance gradient of the plasma gun. For the circuit, the capacitor bank is modeled as a pulse forming line as and v,i is given by (4.2). The effective electric field is shown in Figure 3. Kirchoff's Law for the circuit, the evaluated as the mean voltage gradient between the electrodes. Combining with the accelerator current equation of motion for the plasma slug and the equation for the Coulomb electrode erosion can be written as: determined earlier, the ohmic ileating rate provides an estimate for the plasma resistance, which is then used + =v,-(Rb+R+R+L'v)I iteratively to determine a self consistent value of the voltage gradient between the electrodes. The iterative L'=( lt lln(bl. L,=L'z. R,=R'z( I---L+l--L) procedure yielded a plasma wdtage of approximately \2;,r) \a) " _,A_. A,.,,) 750 V and an ohmic heating r_,te for the plasma of 9 x 10s W. The radiative loss ca!culated as a blackbody radiation assuming a reasonable value of 0.5 for the C aV_ "I L,+,dl'÷' -V,..,-V,., ,--_--t=-(,-1,+,), i>_l, plasma emissivity is 6 x 108 W, indicating that the dt assumed plasma temperature of 4 eV can be sustained by the ohmic heating. The whole procedure may be iterated -d-v_p _ I2-LI: -rh vp-2Copv:pA, dz_ am, to provide a more consistent estimate of the plasma dt m ' dt - ve' _ = mcl p temperature. Finally we check for quasi-neutrality. This requires that where L1, L_ are the transmission inductance (bus-bar the Debye length is small compared with the plasma and the internal inductance of the capacitor) and the dimension, 20 <<L. With the _bove prescription for the time-dependent inductance of the plasma gun, Ci is the capacitance of the capacitor connected to the plasma plasma condition, the Debye length may be checked to be approximately 20 nm, whkh is sufficiently smaller gun, Rh, R_, Rp are the resistances of the transmission than the plasma dimension. (bus-bars), the conductors of the gun, and the plasma sheet respectively, R' is the resistivity of the gun We are now ready to run a lumped element (0-D) conductors, Ai, , Ao, t are time-dependent cross- simulation code to model tile performance of the accelerator, assuming that the plasma will stay together sectional areas of current conduction of the inner and and be accelerated as a "slug". This is done in the next outer conductors (electrodes) of the coaxial plasma gun, section. taking into account the skin depth due to the pulsed nature of the current, b and a are the outer and inner 5 Lumped Element Modeling Results radii of the electrodes respectively. The PFN sections are numbered as section i = 1, 2, 3...... counting from the section nearest to the gun. C, and L, are the capacitance The circuit and the dynamic,,, of the plasma slug is and the inductance of the i-th PFN section. I_ is the simulated using a 0-D plasma :_ccelerator code in which current through L, and V, the voltage on C,. For the AIAA-2002-2194 equation of motion, we have in,:luded the effects of the pfnx_plasma: Plasma velocity 3130 entrainment of the products of ,'lectrode erosion in the CD= 0.001 __/_ plasma as well as the effects of :,kin friction between the 250 plasma and the electrodes. ('o is the skin-friction coefficient The last equation elves the rate of mass 29O entrainment in the plasma dt_v to electrode erosion _-_ C D = 0.01 associated with charge transfer. The coefficient m'E o 1 gives the electrode erosion rate in kg/C of charge > transfer. e_ , CD= 0.1 ---. lo0 13. The code (PFNX_plasma) uses .t4 (1/2) - order Runge- Co = 1 .......... Kutta-Fehlberg differential equation solver. Although the effect of tapering the elector>des with the attendant a i i i variation in L' as a function of 1he plasma current in the 0=5 1 115 2 2h5 3 3L5 4 4.5 gun can be simulated, in order to keep the parametric time (t_s) exploration tractable, a nominal ratio of the radii of the Figure 5. Plasma velocity vs. time outer and inner electrodes is assumed. Figures 4 to 7 show the results of a run wid_ the following circuit pfnx_plasma:PlasmaVelocity 38O parameters: 4 capacitors each er 17.5 pF are connected to the accelerator in parallel and charged to 40 kV. The 250 parallel inductance of the capat itors and the connection to the accelerator is held to 15 nil. Figure 4 shows the current pulse shape versus time, Figure 5 shows the plasma velocity versus time, Figure 6 shows the plasma o 15o velocity versus the length of acceleration. Figure 7 shows the capacitor voltage versus time. The figures show the results for four values of the skin-friction coefficient, Co = 0.001, 0.01, 0.1, and 1. The results show that the velocity goals of :'.00 km/s can be obtained f "Co = 1 if the skin friction coefficient is less than 0.01. If the skin friction coefficient is 0.1 oJ 1,the skin friction has a O0 0.11 012 013 014 015 OIB 017 08 Accelerator Length dramatic effect on the performa,ce of the thruster. Figure 6. Plasma velocity vs. Accelerator Length. pfnx_plasma:InductorCurrent pfnx_plasma:Capacitorvoltage:1 413 ,l // \, 3O \ \ \ 0 O) GO10 • °4 / X.. "co =1 o _'x CD= 0.001 mQ'dO -20 ;/ o's 1 l's _ CD= 1 ""......... time(_,_) 45 -3O 0i5 1_ 1,i5 2_ 2kS 3J 3L5 4= 45 time(_s) Figure 4. Current vs. time Figure 7. Capacitor voltage vs. time. 6 Summary In this paper, we give a discussion of the fundamental plasma physics issues governing the pulsed acceleration AIAA-2002-2194 R. L. Burton and P. J. Turchi, "Pulsed Plasma of a plasma sheet by the self fieid of the driving current. [4] A major shift in paradigm in driving pulsed plasma Thruster," Journal of Propulsion and Power, thruster is necessary if the origil_al goal of accelerating a vol. 14, pp. 716-735, 1998. plasma sheet efficiently to high velocities as a plasma [5] Y. C. F. Thio, E. Panarella, R. C. Kirkpatrick, "slug" is to be realized. Firstly, the plasma interior needs C. E. Knapp, and F. Wysocki, "Magnetized to be highly collisional so that it can be dammed by the Target Fusion in a Spheroidal Geometry With Standoff Drivers," in Current Trends in plasma edge layer (upstream) adjacent to the driving 'vacuum' magnetic field. Sec,>ndly, the plasma edge International Fusion Research - Proceedings layer needs to be strongly ma_netized so that its Hall of the 2nd Symposium, E. Panarella, Ed. parameter is of the order of unity in this region to ensure Ottawa, Canada: NRC Press, National Research excellent coupling of the Lorenlz force to the plasma for Council of Canada, 1999. good magnetic confinement. T1firdly, to prevent and/or [6] Y. C. F. Thio, C. E. Knapp, R. C. Kirkpatrick, suppress the occurrence of se,:ondary arcs or restrike R. E. Siemon, and P. J. Turchi, "A Physics behind the plasma, the region behind the plasma needs Exploratory Experiment on Plasma Liner to be collisionless and extremely strongly magnetized Formation," J. Fusion Energy, 2002, to appear. with sufficiently large H.tll parameter. These [7] R. J. Goldston and P. H. Rutherford, Introduction to Plasma Physics: Institute of requirements are quantified in the paper. Physics, Bristol, 1997. Three new design paratr_cters are introduced [81 S. I. Braginskii, "Transport Processes in a corresponding to these three plasma requirements. The Plasma," in Reviews of Plasma Physics, vol. 1, M. A. Leontovich, Ed. New York: Consultants first parameter, labeled in the p_tper as _'],pertains to the permissible ratio of the diffusive excursion of the plasma Bureau, 1965, pp. 205-311. during the course of the acc_'leration to the plasma longitudinal dimension. The second parameter is the required Hall parameter of the edge plasma region, and the third parameter is the requi_ ed Hall parameter of the region behind the plasma. Experimental research is required to quantify the v.dues of these design parameters. Based upon fundamental theory of the transport processes in plast_a, we provide some theoretical guidance on the cho,_:e of these parameters to help designing the necessary experiments to acquire these data. Finally we remark that the plasma requirements prescribed in the paper need t,; be extended to include the considerations of plasma instabilities of the main plasma, especially the Rayleigh-Taylor instability. This will be treated in future work. References [1] T.E. Markusic, Y. C. F. Thio, and J. T. Cassibry, "Design o| a High-Energy, Two- Stage Pulsed Plasma Thruster," presented at 38th AIAA Joint l'ropulsion Conference, Indianapolis, Indiana, luly 7-10, 2002. [2] J.D. Filliben, "Ele_:tric Thruster Systems. Report CPTR-97-65." Chemical Propulsion Information Agency, .h)hn Hopkins University, Columbia, MD, USA CPTR-97-65, June, 1997 1997. [3] P.J. Turchi, "Directions for Improving PPT Performance," presented at International Electric Propulsion C_,nference, 1997.