' UAH Propulsion Research Center Director and Mechanical

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' UAH Propulsion Research Center Director and Mechanical Powered By Docstoc
					Magnetic and Langmuir Probe Measurements on the Plasmoid Thruster Experiment (PTX)
Syri J. Koelfgen' University ofAlabama in Huntsville (VAH),Propulsion Research Center, ,63225 TechnologyHall,

Hmtsville, AL 35899
Richard Esluidge,' Michael H Lee,: and Adam Martin6 .

NASA Marshall Space Flight Center ( S )Propulsion h e a r c h Center TD40, Hirntsville.AL 35812 M K,
Clark W. a k ' and Peter Fmognari' Hw, University ofAlabama in Huntsville @JAW,Propulsion Research Center, S225 TechnologyHall,

Huntsville, AL 35899
The Plasmoid Thruster Experiment (PTX) operates by inductively producing plasmoids in a conical theta-pinch coil and ejecting them at high velocity. A plasmoid i a plasma with s an imbedded closed magnetic fKkl structure. The shape and magnetic f d d structure of the esrd translating pksmoids have been m a u e with of an array of magnetic field probes. Six sets of two B-dot probes were coostructed for measuring Bz and Be, the axial and azimuthal f . The probes are wound on a square G10 form, and have components of the magnetic " an average (calibrated) NA of 93 x lo-' m*, where N is the number of turns and A is the .7 C * nal area. The probes were calibrated with a Helmholtz coil, driven by a highW voltage pulser to measure NA,and by a signal generator to deternine the probe's frequency response The plasmoid electron number density n dectron temperature T and velocity , , lw s ratio v/c, (where v is the bulk plasma f o velocity and c, i the ion thermal speed) have atso been meamred wt a quadruple Langmuir probe. The Langmuir probe tips are 10 mm ih b g 20-ma diameter stahkss stcd win?, housed in 8 6mcb b g &re n, n aIPmina rod. Measurements on PTX with argon and hydrogen from the magnetic f i l d probes and quadruple Langmuir probe will be prtsented in this paper.

Nomenclature
cross-sectional area OfB-dot p r o b e s collection area of quadruple L.angmuir pmbe electrodes 1,2,3, and 4 magnetic field axial componart of magnetic field a i u h l companeato magoetic field zmta f iontbermalspeed electroncharge electmn-electron collisionmean h e path ion-ion colliiion mean bpath current collected by quadruple Langmuir probe electrodes 1,2,3, and 4 Bohmcurrent t current collected a Langmuir probe tip NASAMSFC GSRP Fellow and UAH G a u t Research Assistant, AIAA Student M m e . rdae ebr NASAMSFC Aerospace Systems Engineer, AIAA Member. NASAMSFC Electrical Engineer. NASAIMSFC Physicist. UAH Propulsion Research Center Director and Mechanical & Aerospace Engineering Professor, AIAA Fellow. 'UAH Graduate Research Assistant.

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current density * electron &urabon currentdensity ion satmalmn current density . Langmuir probe electrode length Debye length electron mass ion mass electron number density number of turns of Bdot probe J-angmuirprobe electrode radius clearance between Langmuir probe electrodes time initial time electron temperatwe in eV bulk plasma velocity Bohm velocity voltage induced in B-dot probe coil potential of Langmuir probe electrodes 1,2,3, and 4 potential difference between probes 2 and 1 applied potential difference between probes 3 and 1 applied potential differencebetween probes 4 and 1 B-dot probe passive integrator output signal plasma potential

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Introduction

HE plasmoid thruster is a pulsed inductive &t e that utilizes the J x B (Lorenk) force to accelerateplasmids and produce thrust (Fig. 1). A piasmoid is a plasma with an i n t d magnetic field structure, also known as a compact toroid.' Plagnoid accelerators have been used for fueling h i o n devicesz4 and their application to space propulsion has been proposed and studied theaeticaily.~' The Plasmoid Thruster Experiment (PTX) is an i experiment to evaluate the use of pIasmoids ix ppukion.' The plasmoids are formed inductively in a conical theta-pinch coil, which eliminates the problems associated with discharging a large current across electrodes to produce and accelerate the plasma. Electrode erosion is a limiting factor in the functional lifetime of many pulsed electromagnetic accelerators, such as the magnebplasmadynamic (MPD) thruster?9 Tbe plasmoid thruster is an option for removing this limitation. Additionally, since the piasmoid has a self-contained o magnetic field and is therefore not connected t any external magnetic field lines, the problem of detachment is nxhced. Magnetic o insulation of the plasma should also lead t reduced thermal losses to the walls. An actual plasmoid lhster would operate repetitively at a Figure 1 PLmroid i Conical . n frequency of 10-100 Hz and would use solid-state switching. In the &Pinch Coil present experiment, oniy a single plasmid is formed and accelerated, PTX is not yet optimized.

T

ILPTX
In PTX, the plasmids are produced in a Pyrex tube, which serves as the vacuum chamber, situated inside of a o single-turn conical theta-pinch coil with a half-angle of 17S0(Fig. 2). The Pyrex tube is connected t a nxtangular vacuum chamber for diagnosis of the exhaust plume. The theta-pinch coil is driven by a 560 nF, 40 kV capacitor bank that is switched by a Perkin-Elmer GP-32B spark-gap switch. 'Ibe coil and capacitor bank constitute a tank (LC) circuit that rings sinusoidally with a peak current of 53 kA at 35 kV charge voltage (Fig. 3). The bank is fired by sending an optical bigger signal to a high-voltage pulser that then triggers the spark-gap switch. When triggered, the spark-gap closes, allowing the capacitor bank to discharge through the theta-pinch coil. A solenoid valve injects propellant into the chamber, before the bank is discharged at a time &. (The time before the bank dwharge at which
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propellant is injected is referred to as the puff valve delay.) The rapidly changing axial magnetic field creates an azimuthal electric field that preionizes the plasma Simultaneously, the plasma is seeded with the magnetic field produced during the first half-cycle of the sinusoidal discharge. When the current swings through zero, the field is reversed and the chamber contains a c l , partially ionized plasma with an imbedded magnetic field. As the od external magnetic field increases in the opposite direction, it r e c ~ ~ e cw t the bias field and the plasma is t sh i compressed and fully ionized.' During the formation process, the interaction of the magnetic field with the plasma induces a large azimuthal current in the plasma The resultant J x B force accelerates the plasmoid away h m the coil and generates thrust. Argon and hydmgen gases were chosen to model heavyweight and lightweight propellant in PTX.

Figure 2. Phsmoid Thruster Experiment

I

I

0

2

I 4

I

I

I

6

8

10

Tims P

Figure 3. PTX Capacitor Bank Discharge

IIL Diagnostics
A variety of diegnosticsam used 011 FTX, including: a a high-speed cordin 220B framing camem (with eight independently triggered CCD arrays; inter-frame s, time as low as 10 n) for imaging and estimating the plasmoid velocity; b. an excluded flux a m y (an array of magnetic field probes and flux loops), for determining the shape of the plasmoid in the coil; c. a light pipe velocimeter (fiber optic cables fed into fast PIN photo diodes), for measuring velocity; d. a heterodyne, quadrature HeNe laser intafixometer, for measuring the line-averaged electron density, n& e. an a m y of magnetic field sensors (B-dot probes), for measuring axial and azimuthal magnetic field; and f. a quadruple Langmuir probe, for measuring the plasmoid electron temperature T, number density n, and velocity ratio v/cm where v is the bulk plasma flow velocity and c,,, is the ion thermal speed. This paper will focus of the B-dot probe array and quadruple Langmuir probe.
A. Internal M o t Probe A m y An a m y of internal B-dot pmbedg" has been cxmstructed and installed in the exhaust chamber, perpendicular to the z-axis (Fig. 4). Six sets of two B-dot p r o b e s meawe the axial and azimuthal magnetic fields (Bz and BB)of the ie plasmoid as it translates past the probe array. The probes were wound with 36 gauge magnet w r on a 3.15 mm square G-10 form (Fig. 4). The probe signals are passively integrated (RC = 20 p)for improved dynamic range. The output signals from the passive integrator, V , are recorded with Acqiris digitizers (&bit, 250 Msamples/s).

The magnetic field measured by each p b e is given by:

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mot

a) Internal M o t Probe Array on PTX Figure 4. Internal M o t Probe Array

b) Internal M o t Probe Array

The Bdot probes were calibrated with a custom-built Helmholtz coil (Fig. 5). The Helmholtz coil is a set of two coaxial current loops with equal radii, separated from each other by a distance equal to that radius. The radius and separation of the loops is approximately2.5 inches. Equal amounts of current flowing in the same direction are applied to the loops, producing an extraordinarily uniform magnetic field inside the volume of the Helmhohz coil. The PTX Helmholtz coil was calibrated with a DC power supply, multimeter, and Hall probe to determine the magnetic field inside the Helmholtz coil as a function of applied current. To calibrate the individual B-dot probes in the array, the Helmholtz coil was driven with a 300 Volt pulser, and the resulting voltage responses of the Helmholtz coil and each B-dot probe were recorded with a digital oscilloscope. The calibrated quantity, NA, of the probes was found to be within 20% of the design value of NA = 10 x (3.15 mm)’ = 9.92 x IO-’m’. Figure 5. Helmholtz Coil The frequency response of the B-dot probes was also assessed by applying a sine wave to the Helmholtz coil at fi-equencies ranging from 1 lcHz to 12 MHz. The resulting Helmholtz coil signal (obtained with a Pearson current probe) and the B-dot probe responses were measured with the oscilloscope and combined to determine NA as a function of frequency. B. Quadruple Lnngmuir Probe A quadruple Langmuir probeI2 has also been constructed (Fig. 6) to make local measurements of the plasmoid electron temperature T,, electron number density n and velocity , -# ratio v/c,,,. Three of the four probes are aligned parallel to the plasma flow (the z-axis); the fourth probe is aligned perpendicular. The Langmuir probe tips are 10 mm long, 0.5 mm (20 mil) diameter stainless steel wires, housed in a 152 mm long, Cbore alumina rod. $, The alumina rod is torr-sealed into a stainless steel tube and + e ? installed at the downstream end of the PTX exhaust chamber through a sliding O-ring seal, so that measurements may be taken along the z-axis. An electrical schematic of the quadruple Langmuir probe is : g shown in Fig. 7. Probe 2 is unbiased, and so it floats to a potential such that it does not collect any current. Probes 3 and 4 are biased Figure 6. Quadruple Lnngmuir Probe at approximately equal voltages (V, and V,) relative to probe 1. Probe 1 is biased above the floating potential and below electron saturation, and emits current. Probes 3 and 4 are biased in the ion saturation region ofthe ideal probe characteristic, and collect current. For both probes 3 and 4, the

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Plasmoid

+

1

3
2

d

-

vdabk V d w s a m r

Figure 7. Quadruple hngmuir Probe Circuit

bias voltage is produced by a variable DC power supply, with 20 pF of capacitance in parallel, in order to source the current on the fast time scale of the experiment. Quadruple Laugmuir probe t h e o ~ y ' ~is~ a combination of ' triple probe theo~y"*'~ and a crossed electrostatic probe techniq~e.'~*'' The measured quantities for data analysis are the currents collected by probes 3 and 4 (13 and I,), and the potential differences of probes 2, 3, and 4 n - . w ~ o l AcqimDig~her relative to probe 1, called V,, V,, and V, respectively, where

v,, = v, -4
and

l , , Simultaneous collection of 1% 4 V,, V , , a d V, yield measurements of T n and v/c,,,. Analysis of the probe response assumes that several conditions are met, including:
a the probe is operating in the collisionless sheath regime, i.e. the condition .

-> 1 is met, where >
AD

e e k is the electron-electron collision mean h e path and AD is the Debye length;
b. the sheath around each probe electrode is thin, as prescribed by
P ' -> 1, where rp is the Langmuir >
AD

probe electrode radius; c. the probe is in the lice molecular regime, so the effect of b s t r e a m i n g particle collisions with the probe can be ignored, such that e e k > l
P '

-

and

- 1 are satisfied, where ii&, >
'P

ii&,

is the ion-ion

collision mean free path; d. the end effect is minimized,which is achieved if the plasma velocity v (the heavy-particle velocity) is small compared t the Bohm velocity v B O hs that there is not a large number of ions reaching the o o probe causing a peak in the measured ion current, such t a the condition ht where L is the length of the probe tip;

L > 50AD -is satisfied,
VBdR

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the m r introduced to Langmuir probe current measurements by probe tip currents is less than approximately 100?4i.e.

I, 1 rp v -= --IB 2 L v -

10.1;and

f. the clearance s between pe electrodes is sufficient so that sheath i t r c i n behveeu adjacent r o b neatos
electrodes is avoided, such that
S -> 250. n,

I h e PTX quadruple Langmuir probe w s designed to ensure t a these conditions w r adequately met under a ht ee expected operating c n i i n . odtos
I . Electron Tempratwe This paper takes a slightly different approach to the derivations of the formulasfor T, and n,h w v r tbe results oee are equivalent t those found in other o To determine an expression for the electron temperature from the quadruple Langmuir probe m a u e e t , we begin with equations describing the cuITent collected by probes 1,2, esrmns and 3:

Z, = J,A, e x p ( 7 ) - JiA,

-Z3 = J , 4 exp --J i 4

(”,”)

where A I , A2, and AS are the current collection areas of probes 1, 2, and 3, V, is the plasma potential, T is the , eprtr nt electron t m e a u ein u i s of electron volts (eV), and J, and 4 are the electron and ion sahrration current densities, as given by:

J, =

2nm,

(7)

w e e ne is the electron number density, e, is the electron charge, me is the electron m s , and Mi is the ion m s . hr as as Since the current emitted by probe 1 is collected by both probes 3 and 4, and since Il f o s in the opposite direction lw of13 and 1, (as shown in Fig. 7),

Il = --(I3 + 1,) = -I3 (1

+?)

.

(9)

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Given that A = A2 =A3, and substituting Eq. (9) into 4.(4), we have:

Il =-Je4 exp

[ [7,")

-:](l+$)*

Since probe 2 is floating and tbefore Z2 = 0, Eq. ( 5 ) reduces t o

Equating Eq. (4) and Eq. (lo), noting that A l = A3, dividing by J, and applying Eq.(1 1) yields:

exp(

7)

-exp[y) =

-[ +$)[
1

exp[

y) 7)]
-exp[ -exp[

.

(12)

Multiplying Eq. (12) by -exp

(-) .(-2), : .
and

and applying Eq. (2) and Eq. (3a), we am left with an

expression for Te (in eV) as a fundion of the measured quantities Z3,, and Va as well as the applied voltage Va: Z

exp[

F) +$I[ [F] ?]I.
- 1 =(1
exp

2. Electron D mt e -y To derive an expression for the electron density, E .(6) is represented as: q

-I3 = Je4exp(;)exp($)-Jt4.

Rearranging Eq. (1 1) into

exp

[3

=: x ep

[+)
,

substituting this into Eq. (14), and using Eq.(2) and E .(3aX we are left with: q 7

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-13=JiA3[exp( T,'d2 )-I]. 'd3 -

Substituting Eq. (8) into Eq. (16, and rearrangin& yields the expression for G: )

-I,

3. Velocity In addition to measurements of Te and ne, the quadruple Langmuir probe also provides a measurement of the velocity ratio v/c, h m the collected currents I3 and I,. For V, = V,, with probe 3 aligned with the flow vector and probe 4 perpendicular to it, the ratio of I3 to 1, has been shown to be"

The velocity ratio v/c, is obtained by itemtion of Eq. (19).

IV.

Experimental Results

The Bdot probe array is mounted on the top of the P'IX exhaust chamber, so the plasmid magnetic field can be measured at various vertical positions in the chamber (Fig. 8). In Fig. 8(a), probe B-d, the third axial Bdot probe in the array, is positioned on the centerline of the theta-pinch coil and chamber. Pmbe B-zl is in the l w s oet vertical position (below the centerline) and B-z6 is in the highest vertical position. In Fig. 8(b), probe B-d is on the centerline. @) Probe B-z5 on CL For the same operating conditions (argon at 6.5 psig manifold pressure injected at a 2600 p puff valve delay), PTX w s run with the Bdot probe array in the two Figure 8. M o t Probe Array Positions in a different vertical positions on two different days. This w s Relation to the PTX Centerbe (CL) a done so that the plasmoid magnetic fields could be mapped over the entire vertical cross-section of the chamber. & February 23,2004 Shot3, the B-dot probe array positioning I shown in Fig. 8(a) w s used, and on February 25,2004Shot 43,the configuration in Fig. 8(b) was used. The axial a and azimuthal magnetic fields as a function of time were obtained for both shots. The magnetic field averaged over several data points about 18.65 p (the time near the axial magnetic field peak) w s then determined for each B-dot a probe, so that the magnetic field could be graphed as a function of vertical position, as each B-dot probe corresponds to a different vertical position in the chamber. The axial magnetic field profile vs. vertical position for the two shots a 18.65 p is shown in Fig. %a). A t Cordin camera photo of the plasmid translating toward the Bdot p b e array is shown in Fig. 9(b). The light pipe
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velocimeter measured plasmoid velocities of 28 kmls on February 23, 2004 Shot 3 and 22 km/s on February 25, 2004 Shot 43. For the same operating conditions, the quadruple Langmuir probe w s also used to measure T, n a , and v/cma a function of time (Fig. 10). s

(a) Bz vs Vertical Position

(b) Cordin Photo from 2-25-04 Shot 43

Figure 9. Plasmoid Magnetic Field v . Vertical Position and Cordin Camera Photograph, 6 3 psig Argon s at 2600 ps delay

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-

Phmoid Tapanbrrn T i
05-19-04 S e t - I

sX1om4T

FlmNddDalitynTuc
05-19-04 sL.1-07

0-

c-

% s

e

321-

4-

f

20I

0I I I

15

20

25

30

1 35

I

10

m

I

1

30

I 40

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50

timzP

h s Ps

Figure 10. Plasmoid Temperature and Density, May 19,2004, Shot 7,6.5 psig Argon at 2600 ps delay Figure %a) is consistent with the axial magnetic fields expected in a plasmoid. Figure 10 shows a maximum electron temperature of 7.6 eV and a maximurn electron number density of 4.9 x lOI9 m-3. At 18.65 p, the temperature is 6.3 eV and the density is 4.0 x lOI9 m-3. In determining the velocity ratio v c the summation term in /, Eq. (19) reaches a constant value after 50 terms, so for n = 0 . 0 the peak velocity ratio for this test w s .5, a approximately 3 2 . For comparison to argon, hydrogen w s used as a lightweight propellant. The axial and azimuthal magnetic a fields in PTX for hydrogen a 38.6 psig manifold pressure, injected 2400 p before the bank discharge, are shown in t Fig. 11. Numbers corresponding to each Bdot probe are placed on their corresponding curve, where “1” denotes the magnetic field curve obtained f b m Bdot probe zl or 81. In Fig. 1 1 we see that the azimuthal magnetic field, BO, reverses direction, which is consistent with the field-reversal characteristic of plasmoids. The noise i the n beginning of the magnetic field plots is pick-up from the discharge of the capacitor bank. Figure 12 shows the electron temperature and density profiles for similar operating conditions. The temperatures a the first and second t peaks are 22 eV and 23 eV. The correspondingdensities at the two peaks are 1 . I x Ido and 1.2 x lo2’ m”. The m-3 velocity ration v/cm the first peak in Fig. 12 is approximately 0.4. on

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-10
I I

I

I

I

I

I

I

I

I

10

a0

30

40

-c

Figure 11. P h o i d Magnetic Fields, May 18,2004, Shot 28,38.6 pig Hydrogen at 2400 ps delay

eprtr Figure 12. Plasm& T m e a u eand Density, June 14,2004, Shot 3,387 pig Hydrogen at 2400 ps delay

V .

Discussion

The magnetic field plots obtained from the B-dot probe array are consistent with plasmoid magnetic field configurations,' so PTX appears to be producing plasmoids. ~n tests resented, the peak electron temperature, the electron number density, and velocity ratio were 7.6 eV, 4.9 x lo-'' ms, and 3.2 for argon, and 23 eV, 1 2 x loem m-3, and 0.4 for hydrogen. Hydrogen p r o d u d higher temperatures and densities, and lower v/c,, than argon, as expected with a lighter gas. The two peaks in the hydrogen temperature and density plots may indicate that two plasmoids are being fimned during a single s o . In addition, some of the azimuthal B-dot probes show ht a magnetic fields changing direction twice, which m y indicate that two plasmoids are W i g formed in successive cycles of the ringing discharge. A large volume of F'TX data, which is suf€iciently reproducible for similar a operating conditions, h s beem collected and is being analyzed.

Acknowledgments
Syri Koelfgen is h d e d by the NASAMSFC Graduate Student Researchers Fkgram (GSRP)fellowship. 'Ibis research was conducted in tbe NASA/MSFC Propulsion Research Center (TD40) laboratories. The authors would like to thank Jeff Richeson, Tommy Reid, and Doug Galloway of Mainthia for their technical support of PTX.

References
'Tuszewski, M , . "Field Reversed Configurations-Review Paper," Nuclear Fusion, Vol. 28, No. 11,1988, pp. 2033-2092. *Hof€inau,A. L,et al., "Inductive Field-Reversed Configuration Accelerator for Tokamak Fueling" Fusion Technology, Vol. 36, Sept 1999. 'Miley, G. H., "Compact tori for alternate fuel fusiin," Nuclear Instrumem and Methods in Physics Research, Vol. 207, NO. 1-2,15 March 1983,pp. 111-120. 'Kawai, K., Pietryk, Z. A., and Hunter, H. T., ''Generation of poloidally rotaspheromaks by the conical theta p s " P b s . Fluiak,Vol. 30, No. 8, Aug. 1987, pp. 2561-2568. 'Jab, R G., Plysics of EfectricPropulsion, McGraw-Hill, 1%8.

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hraque, R E,and Parks, P. B., "Time-Dependent Analysis of the Pulsed Plasnoid E e t i Thruster;"AL4AA?WOM lcrc Con&mme on AdvoncedSEI Technologies,AlAA Paper91-3614, Cleveland, OH,4 6 Sept. 1991. 7Slough,J., "Propagating Magnetic Wave Plasma Accelerator (PMWAC) for Deep Space Exploration," STTR Phase-1 F j Report, 2000. koeKgen, S J., Eskridge, R, Hawk, C. W., . Lee, M. I€, Martin, A, and Smith, J. W., "A Plasmoil Thruster for Spece P r ~ p u l s i i " AUA/ASMEMWASEE Joint Pmpulsion Conference & Exhibit, AIAA Paper 20034995 Hmtsville, AL, 2 3p 0

23 July 2003. gMyer~,R M., e d ," ab d phenomena m a Low-power ~agaetoplasnadynam~: t . ctoe . lluuskr," &d Propvlsion and of Power, VoL 7 No. 5, Sept.-od 1991, pp. 760-766. , '%utchhm, I H., Princiules of P . h Diupmlia,Cambridge U i e s t Press, 1 8 . nvriy 97 "HwIdMow, R I€, and Leonard,S L., P l a n a LXupstic T e h k p e s , Academic Press, 1%5. . "Burbn, R I DeIMedioo, S G ,and AoQews J. C., "Application of a Qusdnrple Probe Tscbnique to MPD Thruster , . , . . Plume ueasunmcnts;"JorsnrJofPropulsionmdPower, Vol. 9, No. 5, Sept.-Oct. 1995,pp. 771-777. "Bdbm, S. A, "ExitPlane Plasma Measurements of a Low-Power Hydrazine Arcjet;" W D Dkrtahon Univ. of Illinois, .. , U * 19. 96 -Kl, !e y A. J., and Jahn, R G., T h e Application of the Triple Probe Metbod to MPD Thruster Plumes," 21" A L 4 A / D G W !I r z t e m d d EIectrc Pmpulsbn Co4erence, AIAA Paper 90-2667,OrlSnQ, FL, 18-20July 1990. I5cben,S. L,and S e w T., ''Insbmtaneous Direct-Display System of P h Perameters by M a s of Triple Probe," en Journal of Aplpled Physics, VoL 3 ,No. 8, Aug. 1965,pp. 2363-2375. 6 '%mal, M, "Theory of Current Collection of Moving Cylindrical Probes," J0M;lal o Applied Physic, Vol. 3 ,No. 6 June f 5 , 1964, pp. 1697-1703. '7J0hnsoq B. H,and Murphree, D. L., ''Plasma Velocity Determination by Elecbostatic Probes," AUA J d , Vol. 7 Od. . , 1 9 pp. 2028-2030. %,

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