NASA/ TP-2003-212341 

Magnetic Flux Compression Experiments 

Using Plasma Armatures 

M. W. Turner and C. W. Hawk 

Propulsion Research Center, The University of Alabama in Huntsville, 

Huntsville, Alabama 

R.J. Litchford 

Marshall Space Flight Center, Marshall Space Flight Center, Alabama 

National Aeronautics and 

Space Administration 

Marshall Space Flight Center MSFC, Alabama 35812 

March 2003 
Acknowledgments 

This work was sponsored by the Advanced Propulsion Research Project Office, Advanced Space Transportation Program, 

NASA George C. Marshall Space Flight Center. M.W. Turner also acknowledges the financial support of the NASA Graduate 

Student Researcher Program. The NASA Principal Investigator was Ron J. Litchford. 

~ 

TRADEMARKS 

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Available from: 

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(301) 621-0390 

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528.5 Port Royal Road 

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(703) 487-4650 

.. 

11 
TABLE OF CONTENTS 

1 . INTRODUCTION ........................................................................................................................... 

2 . EXPERIMENTAL APPARATUS .................................................................................................... 

2.1 High-Voltage Capacitor Discharge Bank .................................................................................. 2.2 Pulse Plasma Gun ...................................................................................................................... 

2.4 Inductive Probe ......................................................................................................................... 

2.3 Optical Probes ........................................................................................................................... 

3 . PLASMA JET EXPERIMENTS ...................................................................................................... 

3.1 Circuit Discharge Characteristics .............................................................................................. 

3.2 Plasma Jet Velocity Distribution ............................................................................................... 

3.3 Plasma Jet Electrical Conductivity ............................................................................................ 

4 . CONCLUSIONS ............................................................................................................................. 

REFERENCES ..................................................................................................................................... 

1 

3 

8 

8 

8 

9 

13 

... 

111 
LIST OF FIGURES 

1 . 

2 . 

3 . 

4 . 

5 . 

6 . 

7 . 

8 . 

9 . 

IO . 

11 . 

12 . 

13 . 

I4 . 

Simple radial-mode configuration for basic experimental study of magnetic flux 

compression processes using a pulse plasma gun source ..................................................... 

Configuration for plasma jet source characterization experiments ....................................... 

Schematic of high-voltage capacitor discharge circuit . The major component 

specifications are 30-kV133-mA dc power supply; 60-kV12- to 8-pF capacitor bank; 

40-kV1125-A relays; 30-kV power resistors (R. =100 kR. R8lO kR. R, =IO Ma); 

and 30-kV-spark gap switch .................................................................................................. 

Assembly drawing of the 30" conical pulse plasma gun and photographs 

of the assembled units ........................................................................................................... 

Illustration of inductive probe principle of operation . The plasma jet displaces the field 

lines of the excitation coil and induces an electromotive force in the search coil . The 

degree of field displacement can be correlated with plasma jet electrical conductivity ....... 

Diagram of parameters relevant to the mathematical analysis of probe operation ............... 

Detailed design drawing of probe ......................................................................................... 

Measured coil current and field intensity waveforms ........................................................... 

Illustration of standard and push-pull search coil configurations . The critical damping 

resistance is R -1 kR-m ........................................................................................................ dSchematic of experimental apparatus used for probe calibration . A light-gas gun 

was used to fire a IO-cm-diameter aluminum slug through the probe where velocity 

was inferred from the deflection of a laser beam .................................................................. 

Measured response function for standard search coil configuration .................................... 

Gaussian fit of response function for standard search coil configuration ............................. 

Measured discharge current waveform for the pulse plasma gun circuit at 27 kV ............... 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

Ensemble-averaged optical probe waveforms at 25- and 27-inHg vacuum . Probes 

are located at 0. I. 2. 3. 4. and 5 cm from gun exit ............................................................... 27 

V 
I LIST OF FIGURES (Continued) 

I 

15 . 

16 . 

Plasma jet axial velocity distribution at 25- and 27-inHg vacuum ....................................... 

Measured probe response at 27-inHg vacuum and a discharge voltage of 27 kV ................ 

28 

29 

LIST OF TABLES 

~ 

1 . Summary of inductive probe measurement .......................................................................... 9 

Vi 
LIST OF ACRONYMS AND SYMBOLS 

emf electromotive force 

Hg mercury 

MHD magnetohydrodynamic 

MSFC Marshall Space Flight Center 

UAH The University of Alabama in Huntsville 

vii 
NOMENCLATURE 

I 

Hz 

I 

L 

Lc 

LP 

1 

m 

I N 

I n 

RP 

S 

t 

i U 

magnetic flux density 

capacitance 

diameter 

frequency 

distribution function 

measured signal 

magnetic field 

longitudinal magnetic field 

field coil current 

calibrated field coil current 

kernel 

length 

inductance 

coil length 

plasma inductance 

length of the conductive region behind the shock 

mass 

number of coil turns 

number of capacitors 

resistance 

bleed resistance 

charging resistance 

dump resistance 

magnetic Reynolds number 

plasma resistance 

distance from the search coil to the shock 

time 

velocity of the shock 

... 

Vlll 
NOMENCLATURE (Continued) 

U 

UC 

V 

X 

A 

Vl 

w2 

particle velocity behind the shock 

velocity of the calibration slug 

voltage 

calibration response function or kernel 

peak value of calibration slug response 

peak value of the calculated voltage curve 

output signal of the search coil 

energy 

distance from the search coil to an arbitrary point behind the shock 

differential change 

magnetic permeability of material under consideration 

magnetic permeability of free space 

relative magnetic permeability with respect to free space 

distance from an arbitrary location x to the shock 

resistivity 

calibrated resistivity of slug 

electrical conductivity 

maximum conductivity 

characteristic plasma electrical conductivity 

calibrated slug conductivity 

area of measured voltage pulse curve 

area of calibration response function for slug pulse 

integrated induced voltage signal 

function dependent on the conductivity distribution 

function dependent on the conductivity distribution 

ix 
TECHNICAL PUBLICATION 

MAGNETIC FLUX COMPRESSION EXPERIMENTS USING PLASMA ARMATURES 

1. INTRODUCTION 

Practical deep space mission scenarios require extremely high energy density vehicle concepts, and 

magnetic flux compression reactors appear to offer one plausible means of meeting the rigorous propulsion 

and power requirements. Litchford et al., for instance, discuss several pulsed magnetic flux compression 

reactor configurations of potential interest. 1 

In these devices, the expanding diamagnetic plasma cloud produced by a detonation compresses 

the initial magnetic flux within a semienclosed reactor structure until the expansion is ultimately reversed 

and expelled by increasing magnetic pressure. Reactors of this type can accomplish two important 

functions: (1) Collimation and reflection of the hot diamagnetic plasma for direct thrust production with 

minimal ablative effects; and (2) electric power generation by direct energy conversion. Preliminary 

system-level assessments indicate that such devices could yield the specific power and spacecraft acceleration levels deemed necessary for practical exploration and development of the solar system. 

Of crucial importance to the complex underlying magnetohydrodynamic (MHD) processes in field 

compression reactors is the magnetic Reynolds number (&), the value of which depends upon the product 

of plasma electrical conductivity and velocity. Indeed, flux diffusion losses into the plasma will be severe 

unless R,>>l. As such, a thorough understanding of MHD phenomena at high magnetic Reynolds numbers is essential to the reliable design and operation of flux compression reactors. 

Of equal importance is the potential development of Rayleigh-Taylor or interchange instability as a 

heavy fluid (Le., plasma) is decelerated by a light fluid (Le., magnetic field).2-s In this type of instability, 

the fluids tend to interchange positions into a lower energy state via classic bubble-and-spike formation 

and can result in the ejection of high-speed jets from the main plasma cloud which may impact the reactor 

wall with disastrous consequences. It is therefore essential to have a reliable working knowledge of the 

origin and mechanisms of this class of instability, which can assume various forms depending upon the 

magnitude of the ion Larmor radius. 

When the Larmor radius is small compared to density gradients and wavelengths, the RayleighTaylor growth rates for the MHD fluids are the same as for ordinary fluids having greatly disparate densities. This was first clearly observed in the classic laboratory plasma gun experiment of Dickinson et aL6 On 

the other hand, when the ion Larmor radius takes on values comparable to the density gradient length, the 

MHD instability regime is predicted to stabilize. Ironically, it has been discovered that as the ion Larmor 

radius becomes large compared to the characteristic dimensions of the plasma (Le., when the ions become 
effectively unmagnetized while the electrons remain effectively magnetized), an entirely new form of 

interchange instability emerges having a growth rate larger than the original MHD in~tability.~ 

As a means of acquiring a deeper level of understanding with respect to these phenomena, the 

authors have embarked on a series of simplified flux compression laboratory experiments designed to shed 

insight into the physical processes of critical importance. Specifically, we intend to explore a plasma gun 

configuration similar to that introduced by Dickinson et al. in which the ejected plasma impacts a solid 

metal barrier and forms a radially expanding plasma armature, which in turn interacts with an applied axial 

magnetic field.6 Following a previous suggestion of Litchford et al.,' it is also deemed desirable to explore 

high-temperature superconducting materials for use as a stator compression surface. The basic experimental configuration of interest is shown in figure 1. 

I As a prelude to this intensive basic scientific study, exploratory experiments have been carried out 

as part of an attempt to quantify the magnetic Reynolds number characteristics of the plasma jet source. In 

time-of-flight measurements using optical probes and the electrical conductivity was measured using a 

previously developed inductive probing technique.8 This Technical Publication reports the design and 

development of the basic laboratory apparatus and documents the preliminary results from our initial plasma 

jet source characterization study. 

I this experimental effort, illustrated schematically in figure 2, the plasma jet velocity was deduced from 

2 

1 
2. EXPERIMENTAL APPARATUS 

The basic apparatus for the plasma jet source characterization study is a high-voltage capacitive 

discharge circuit coupled with an ablative conical cavity pulse plasma gun which fires into an evacuated 

cylindrical tube. An inductive probe is used to measure electrical conductivity, and fiber optic probes 

mounted in the tube wall are coupled to fast response detectors for time-of-flight measurement of jet 

velocity. The essential subsystems are described in detail in sections 2.1 through 2.4. 

2.1 High-Voltage Capacitor Discharge Bank 

A high-voltage capacitive discharge circuit was designed for general-purpose duty as shown schematically in figure 3. It consists of a bank of 2-pF, 60-kV capacitors which can be combined in parallel to 

form a group having a total capacitance of nC where n=l, 2,3, or 4 and C=2 pF. The bank was configured 

with n=l for all tests in this particular series of experiments. 

The circuit incorporates a 30-kV, 33-mA high-voltage dc power supply as a charging source for the 

bank, and various 40-kV-rated relays permit remote operation of the charge-discharge cycle. For example, 

charging is accomplished by opening the normally closed dump relay, closing the normally open source 

isolation and ground isolation relays, and supplying power through a charging resistor (R,=100 kQ) which 

limits the maximum current draw. Once the bank reaches the desired voltage level, the source isolation and 

ground isolation relays are opened as a means of isolating the circuit, and the discharge is triggered with a 

pulse transformer which drives a 30-kV-rated-spark gap switch. If the circuit fails to discharge, the stored 

energy can be rapidly and safely dissipated in a power resistor (&=I0 kQ) by simply deactivating the 

dump relay. A bleed resistor (R,=10 Ma) is also incorporated into the circuit to provide continuous drainage of energy and to ensure that the bank does not become inadvertently charged. 

The high-voltage capacitive discharge circuit is coupled with the pulse plasma gun through a simple 

coaxial transmission line. A high bandwidth, 10,000: 1 voltage divider and a O.OOI-mV/A current transducer are also available for monitoring the bank and for accurate measurement of discharge waveforms. 

2.2 Pulse Plasma Gun 

The simple pulse plasma gun developed for the present experiments is geometrically similar to 

Dickinson's original pulse crater gun.6 The basic design is essentially that of a conical cavity pulse plasma 

thruster in which a pin electrode (Le., cathode) is situated at the apex of the cone and a ring electrode (i.e., 

anode) is situated at the base of the cone. The conical insulator is machined from DuPont'sTeflon@, which 

serves as an ablative propellant source during high current discharge. 

Two plasma guns were designed and constructed with included cavity angles of 30" and 60", 

respectively. The assembly drawing for the 30" conical plasma gun is shown in figure 4 along with photographs of the assembled units. 

3 
2.3 Optical Probes 

The pulse plasma gun is mated to an evacuated tube having fiber optic probes embedded at 1/2-cm 

intervals along its length. The design includes a total of 12 probes yielding an active probing length of 

6 cm. These fiber optic probes are connected to fast rise time (1 ns) detectors whose output signals are 

edge may not be spatially correlated with optical emission; nevertheless, the time of flight of optical emission is considered a reasonable basis for estimating plasma jet velocity. 

I recorded with high bandwidth digital oscilloscopes. The authors recognize that the true plasma jet leading 

2.4 Inductive Probe 

In the current set of experiments, an attempt was made to measure plasma jet electrical conductivity using a weakly intrusive inductive probing technique that was originally developed for shock wave 

~tudies.~ In previous related work, the authors succeeded in adapting this inductive probing scheme for 

application to plasma jets emitted from shaped charge explosives? and it was believed that the technique 

could also be successfully adapted for the pulse plasma gun source. A brief summary of inductive probe 

theory, design, calibration, and operation is provided below, and the reader is referred to the original sources 

for further details. 

, 

I 2.4.1 Fundamental Principles of Operation 

The inductive probe, illustrated in figure 5, is a simple electromagnetic system consisting of two 

adjacent coils wound on a nonmagnetic tube. The field coil (i.e., solenoid) is first excited by a dc power 

supply in order to introduce an axisymmetric magnetic field inside the tube. The resulting field lines are 

illustrated in figure 5. A small search coil is situated slightly forward of the excitation coil to pick up the 

electromagnetic disturbance produced by passage of the plasma jet. 

As the plasma jet enters the field region, it displaces the magnetic field lines due to its diamagnetic 

properties. That is, eddy currents are established in the plasma which resist magnetic field penetration. 

This perturbation, or compression, of the magnetic field lines induces an electromotive force (emf) in the 

search coil. The magnitude of the emf is representative of the degree of field displacement and, given the 

jet velocity, can be correlated with the plasma electrical conductivity. Actual recovery of the electrical 

conductivity distribution from the induced emf signal requires the difficult inversion of a Fredholm integral equation of the first kind, as shown in section 2.4.2 which is devoted to the mathematical theory of 

probe operation. 

In principle, the plasma conductivity can be directly calculated from the coil geometry and the 

known jet velocity; however, Lin et al. have demonstrated that it is much easier to obtain the probe 

response function empirically by firing a metallic slug of known conductivity through the de~ice.~ 

I 2.4.2 Mathematical Theory of Operation 

Following the mathematical analysis of Lin et al. for the inductive probe, we arrive at a Fredholm 

integral equation of the first kind for the conductivity (o)~ 

I 4 
where @(s) is the integrated induced voltage signal on the search coil, 

@(s) = jsV(s) ds , 0 

and V(s) is the output signal of the search coil. A diagram of the parameters relevant to the mathematical 

analysis is given in figure 6. The major parameters are the length of the conductive region behind the shock 

(Z), the distance from the search coil to the shock (s), the distance from the search coil to an arbitrary point 

behind the shock (x), the distance from an arbitrary location x to the shock (e=+.), the velocity of the 

shock (U), the particle velocity behind the shock (u), the field coil current during a test (I), the velocity of 

the calibration slug (u,), the field coil current during calibration (Ic), the electrical conductivity of the 

calibration slug (o,), the calibration slug response function or kernel (V,), and the unknown plasma electrical conductivity distribution ( oo). 

The Fredholm integral equation of the first kind has the general form 

where g(s) is a known function (Le., the measured signal), K(s,e) is the kernel, andfit) is the unknown 

distribution function. In general, closed-form analytical inversions can be obtained only for special functions, and one must resort to numerical methods. 

Numerical deconvolution algorithms for recovering fie) are generally based on a linear vector 

space representation of equation (3). Turner et al. discuss the numerical inversion issues associated with 

this inversion, including the severe instabilities commonly encountered with the Fredholm integral equation of the first kind, and they demonstrate the application of a constrained linear inversion technique to 

this problem. 

In many cases, however, interpretation of the experimental data can be facilitated by an approximate treatment of the integral equation. For example, Lin et al. showed that it is possible to express the 

ratio between the maximum conductivity (6) behind the shock wave and the calibration slug conductivity 

(0,) as 

and 

5 
I 

where Vcp and QC are the peak and the pulse area of the calibration slug response function, respectively; Vp 

dent on the conductivity distribution. Various results for different conductivity distributions are tabulated 

in the 1iteratu1-e.~ 

l and Q, are the peak and the pulse area of the calculated voltage curve; and 'y, and 'y2 are functions depenFor the special case where the conductivity distribution is a step function and the probe response 

function is Gaussian, both 'y, and ly2 are unity. When the conductivity distribution deviates from a step 

function, it turns out that 'y, and 'y2 are equal to unity plus a small correction term. This mathematical 

behavior is extremely useful for the purpose of estimating the characteristic plasma jet conductivity 

encountered in our experiments. 

2.4.3 Probe Design 

The detailed design of the inductive probe is shown in figure 7. The basic structure is a nylon coil 

form which has been machined to accept two coil windings. The coil form has a bore diameter of I .3 in and 

a wall thickness of 0.125 in. A 900-turn magnet field coil was wound from No. 18 enameled magnet wire. 

The resulting solenoid has a length of I .5 in and an outer diameter of 3.8 in. The search coil consists of dual 

25-turn windings of No. 28 enameled magnet wire. These windings can be connected in series or in a pushpull configuration as demonstrated by Lin et 

I 

I 

I 

The excitation field coil was designed to produce a solenoidal magnetic field between 0.5 and 1 T 

inside the bore. A 20-kW dc power supply was used to drive the excitation coil at 300 V (maximum), and 

the operating time was limited to 1 s in order to minimize resistive heating. 

The field coil was calibrated by measuring the time-varying current when activated by a solenoid 

switch. The time-varying magnetic field in the bore was also measured using a Hall probe connected to a 

Gauss meter. The resulting waveforms are shown in figure 8 at maximum applied excitation voltage. We 

observed a rise time of 20 ms, a peak current of 56A, and a peak field intensity of 0.8 T. Reproducibility of 

these waveforms was excellent. The waveforms remained relatively flat around the peak values for =15 ms 

after which they gradually decayed and stabilized to =63 percent of their maximum values. Therefore, a 

15-ms target window was identified for probing at maximum field strength. 

In the shock tube experiments of Lin et ai., electrostatic effects were encountered which were 

associated with nonuniform charge distributions in the ionized gas.9 This effect, while of great physical 

interest, introduces a finite capacitance between the search coil and the plasma and could lead to spurious 

signals. This difficulty was overcome by connecting dual-turn windings in a push-pull configuration, as 

shown in figure 9. The center tap is connected to ground and I-kR shunt resistors are used to achieve 

critical damping. In this configuration, the capacitive pickup from the two ends of the coil is canceled 

while the inductive pickup is unaffected. A similar strategy was implemented in our probe design so that 

we are able to utilize either a 50-turn standard connection or a dual 25-turn push-pull connection, as needed. 

I 

2.4.4 Probe Calibration 

In order to calibrate the inductive probe, it is necessary to fire a metal slug of known electrical 

conductivity through the probe. The velocity of the slug must also be measured. To accomplish this 

6 
requirement, a simple compressed light-gas gun was developed using 150 psi helium stored in a small 

cylinder. The helium was released into the gun breech by a solenoid-actuated valve, which could be triggered electronically, and a 4-in-long, 1 -in-diameter aluminum cylinder was propelled down a plastic barrel 

and through a glass tube holding the probe assembly. The resistivity of the aluminum was p=3x104 R-m. 

The velocity of the slug was inferred from the deflection of a laser beam. A digital computer-controlled 

firing sequence was implemented incorporating appropriate timing delays, and the various signal 

waveforms were captured on a digital oscilloscope. A schematic of the calibration apparatus is shown in 

figure 10. 

The timing for the calibration experiment was crucial. For example, to hit our target window it was 

necessary to accurately trigger the excitation field coil 20 ms before the slug entered the active probe 

region; otherwise, the probe would not be at maximum field strength at the appropriate moment. This 

timing problem was summarily resolved after several test shots. 

To measure the slug velocity, we directed a laser beam through the glass tube and onto a fast 

response optical detector. When the slug entered the glass tube, the laser beam was deflected and the 

detector signal fell. After slug passage, the beam path was cleared and the detector signal returned to its 

normal value. Therefore, we could determine the time of flight of the slug past the beam and infer the 

velocity from the known slug length. The captured detector waveforms indicated a time of flight of 

At4 ins, and we deduced a slug velocity of 2,150f164 cm/s. 

The measured response function of the standard configuration search coil (50 turns) is shown in 

figure 11. This waveform, which represents an ensemble average of seven shots, consists of two perturbations. The first is the entrance perturbation associated with initial field displacement as the probe enters the 

active probe region. The second is the exit perturbation associated with restoration of the original field as 

the slug leaves the active probe region. When the slug fills the active region completely, there is no signal 

since the displaced field is quasi-steady. Only the entrance portion of the response function is needed for 

inversion purposes. 

The response function is very nearly Gaussian as can be seen from the fit shown in figure 12. Here, 

we have transformed to spatial coordinates using the known slug velocity. We observe that the response 

function reaches a peak value of ~1.3 V when the leading edge of the slug is ~3.5 cm past the search coil. 

The standard deviation of the Gaussian fit is 1.8 cm, indicating that the probe has an effective resolving 

power of 4 cm. This is more than sufficient to resolve the leading portion of a plasma jet. 

For the push-pull search coil configuration, a response signal is obtained from each segment of the 

search coil circuit where the output from each segment is referenced to the grounded center tap. Therefore, 

the entrance perturbation is positive for the push segment and negative for the pull segment. The exit 

perturbations are also of opposite sign. The response functions are again found to be nearly Gaussian, and 

the peak signal values are exactly half of that obtained for the standard configuration, as expected. The 

effective resolving power is also identical to the standard configuration. 

7 
3. PLASMA JET EXPERIMENTS 

To characterize the plasma jet source, two series of tests were carried out using the simple experimental setup illustrated in figure 2. In all of these tests, the vacuum chamber was pumped down to moderately low pressure (i.e., 25- to 27-inHg vacuum) with natural air as the background gas. The primary 

objective of the first series of tests was to obtain the plasma jet axial velocity distribution; therefore, they 

were conducted with the inductive probe removed. The primary objective of the second series of tests was 

to measure plasma jet electrical conductivity with the inductive probe installed near the exit of the plasma 

gun. The results are discussed in sections 3.1 through 3.3. 

3.1 Circuit Discharge Characteristics 

The nominal discharge voltage was 27 kV for all of the experiments with C=2 pF. This implies the 

release of W=1/2CV2=729 J, a large fraction of which is delivered to the plasma jet. The intensity of the 

resulting discharge was clearly evident from the high levels of erosion experienced by the plasma gun as 

determined from posttest inspections. 

The measured discharge current waveform from a typical shot is shown in figure 13. A peak current 

of 250 kA was observed with a ring-down time of ~125 ps. The ringing frequency was 4.0 kHz. The 

resulting estimate for effective inductance, assuming a series LRC circuit model, indicates a need to reduce 

the inductance of the power delivery transmission line. Such modifications will be attempted prior to the 

initiation of follow-on experimental study. 

3.2 Plasma Jet Velocity Distribution 

With the inductive probe removed from the experiment, a series of shots were made in which the 

output signals from selected optical probes were recorded with digital oscilloscopes. The selected probe 

positions were located at 0, 1,2, 3,4, and 5 cm from the plasma gun exit. 

Initial tests were carried out at 25-inHg vacuum to establish a baseline reference. It was quickly 

determined from the resulting data, however, that the plasma jet velocity was much lower than the targeted 

high, we undertook a second series of shots at 27-inHg vacuum. The inferred velocities improved dramatically but were still lower than the anticipated target value. 

I value of I@ m/s. Believing that such poor performance was a direct result of the backpressure being too 

The ensemble-averaged optical probe waveforms for both backpressures are shown in figure 14, 

and the inferred plasma jet velocity distributions, based on the time difference between rising edges, are 

provided in figure 15. At 25-inHg vacuum, the maximum velocity is =2 km/s, and at 27-inHg vacuum, we 

observe an increase to ~4.5 km/s. Although the velocity levels fell short of expectations, a slow axial 

velocity decay characteristic was achieved, as desired. Clearly, lower backpressures are needed to obtain 

higher velocities, but lower backpressures may also tend to reduce jet momentum since there will be less 

I ejected mass. 

8 

i 
Unfortunately, attempts to obtain shots at lower backpressures were not successful at this time, 

apparently due to arcing effects inside the vacuum chamber. Further design modifications will be necessary before it will be possible to obtain reliable velocity data in a lower pressure regime. 

3.3 Plasma Jet Electrical Conductivity 

The final series of tests were carried out with the inductive probe installed in an attempt to measure 

plasma jet electrical conductivity. In these tests, the search coil was located =1 cm from the plasma gun 

exit. This location was selected based on the criteria that the ring-down process be completed before the 

plasma jet enters the region of influence of the probe. The previous velocity measurements along with the 

measured discharge current waveform permitted a preliminary estimate to be made for the appropriate 

search coil location. 

Because the electrical conductivity was anticipated to be relatively high, the inductive probe tests 

were performed at low excitation coil current. The measured value was nominally 13 A. This was sufficient 

current to produce ~0.2 T in the active probing region. It was felt that higher fields would only make the 

measurement more intrusive without benefiting sensitivity. 

To avoid any possible electrostatic effects on the probe measurements, we also elected to utilize the 

push-pull search coil configuration. During initial testing, however, the search coil signal was subject to an 

extremely high level of noise, and extraction of a meaningful signal proved impossible. After expending 

much effort in shielding the signal wires, a waveform was finally acquired in which we had some level of 

confidence. Unfortunately, attempts at follow-on testing to check for repeatability were not possible due to 

failure of the excitation coil power supply. 

The best measured inductive probe signal was obtained at 27-inHg vacuum with a discharge charge 

voltage of 27 kV. The resulting waveform (push coil only) is shown in figure 16 following subtraction of 

the ring-down noise and transformation to the spatial coordinate. The pull-coil waveform is symmetrical 

with the push-coil waveform about the abscissa and is not shown. The maximum amplitude of probe 

response was Vp=4.8 V. 

The reduced data for this test are summarized in table 1 based on application of both the peak ratio 

method, equation (4), and the peak integral method, equation (5). It is explicitly assumed that ty, and ty2 

are approximately unity. In general, the integral ratio method is expected to yield a better approximation 

since ty.. should exhibit less deviation from unity in all cases. 

Table 1. Summary of inductive probe measurement. 

Parameter Dimension Peak Ratio Integral Ratio 

U km/s 4 

cT* u/ocuc 1 0-2 17 

cT* kS/m 30 

pcT* U m-' 150 

o*/cTc 1 0'4 9 

4 

13 

24 

43 

21 0 

9 
The peak electrical conductivity was found to be =30 kS/m based on the peak ratio method and 

=42 kS/m based on the integral ratio method. Thus, p&u=150 to 210 m-l. This implies that a range 

R,=3 to 5 is achievable with our laboratory scale apparatus. 

10 

I 
4. CONCLUSIONS 

To summarize, we note that exploratory experiments have been carried out in an attempt to quantify the magnetic Reynolds number characteristics of a simple ablative pulse plasma gun. The jet velocity 

was inferred from time-of-flight measurements using optical probes, and the electrical conductivity was 

measured using a previously developed electrodeless inductive probe. Using air at 27-inHg backpressure, 

measured velocities were found to approach 4.5 kmls, and measured conductivities were in the range of 

30 to 40 kS/m. This implied the attainment of magnetic Reynolds numbers in the range of 3 to 5 for our 

small-scale experimental apparatus. 

Therefore, it may be concluded that this pulse plasma gun source will provide suitable magnetic 

Reynolds numbers for supporting an intensive scientific study of magnetic flux compression using a rather 

simple laboratory configuration. Planned modifications to the power delivery transmission line and vacuum 

insulation design should permit the attainment of higher jet velocities at lower backpressures with the 

potential for increasing the magnetic Reynolds number range even further. 

11 
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Space Flight Center, AL, January 2001 ; AIAA Paper 2000-2669, June 2000. 

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5. Chandrasekhar, S.: Hydrodynamic and Hydromagnetic Instabilities, Clarendon Press, Oxford, 196 I. 

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Grun, J.; Hassam, A.B.; and Huba, J.: “Large-Larmor-Radius Interchange Instability,” Phys. Rev. Letters, Vol. 59, No. 20, pp. 2299-2302, November 1987. 

8. Turner, M.W.; Hawk, C.W.; and Litchford, R.J.: “Inductive Measurement of Plasma Jet Electrical Conductivity,” NASA TP-2001-210794, Marshall Space Flight Center, AL, January 2001 ; AIAA Paper 

2000-3369, July 2000. 

9. Lin, S.-C.; Resler, E.L.; and Kantrowitz, A.: “Electrical Conductivity of Highly Ionized Argon Produced by Shock Waves,’’ J. App. Phys., Vol. 26, No. 1, pp. 95-109, January 1955. 

13 
14 

,- Superconductor Stator 

~ 

A 

Vacuum 

Chamber 

A 

Copper 

Barrier 

I 

L 

Triggered Spark Gap Solenoidal 

Excitation 

Coil 

Figure 1. Simple radial-mode configuration for basic experimental study of magnetic 

flux compression processes using a pulse plasma gun source. 
lJ 

Figure 2. Configuration for plasma jet source characterization experiments. 

15 
Figure 3. Schematic of high-voltage capacitor discharge circuit. The major component 

specifications are 30-kV/33-mA dc power supply; 60-kV/2- to 8-pF capacitor bank; 

40-kV/125-A relays; 30-kV power resistors (R,=100 kR, R~l0 kR, R,=10 MR); 

and 30-kV-spark gap switch. 

16 
Figure 4. Assembly drawing of the 30" conical pulse plasma gun and photographs 

of the assembled units. 

17 
f 

L 

m 

W 

cn 

Figure 5. Illustration of inductive probe principle of operation. The plasma jet displaces 

the field lines of the excitation coil and induces an electromotive force in the 

search coil. The degree of field displacement can be correlated with plasma jet 

electrical conductivity. 

18 
I 

I 

\ 

I 

I - -I--- 

Figure 6. Diagram of parameters relevant to the mathematical analysis of probe operation. 

19 
0 

Ln 

N 

7 

0 

c 

-F- 0 

0 

0 

tt 

T 

0 

10 

N 

7 

0 

N 

cu 

I 

i 

i 

i 

I 

I 

I 

I 

t 

I 

I 

I 

I 

I 

- 

0 

c? 

0 

I 

0 

0 

0 

c3 

09 

Figure 7. Detailed design drawing of probe. 

20 
60 

50 

n 

5 L= 40 

2 

'0 30 

L 

3 

0 

0 

I= 

0 

a 

- 

.- 

.c, 

.c, .- 

20 

W 

10 

0 

- 

- 

- 

- 

- 

- 

- 

I I ~1 

I -r-~---IL - - -Current (A) 

--- 

I - ,% T 0.9 Magnetic Field (T), H,- 

r /I I 

1 

/ 

1 0.7 

z 

0.6 2 

% 

0.5 

0.4 7 

0.3 

0.2 

0.1 

P, 

0 

CD 

n 

W 

Target I 

I 

I 

Window I 

I ?.I I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

-1 0 0 10 20 30 40 50 

Time (ms) 

Figure 8. Measured coil current and field intensity waveforms. 

21 
Standard Configuration Push-Pull Configuration 

Figure 9. Illustration of standard and push-pull search coil configurations. The critical 

damping resistance is R8l kQ-m. 

I 22 
Figure 10. Schematic of experimental apparatus used for probe calibration. A light-gas gun 

was used to fire a 10-cm-diameter aluminum slug through the probe where 

velocity was inferred from the deflection of a laser beam. 

23 
1.4 - Slug Entrance Perturbation 

Calibration Response Function 

Seven-Waveform Ensemble Average 

Standard Configuration 

L, = 10.2 cm 

u, = 2,150 &I64 cm/s 

p, = 3( 10)-8 Q-m 

a 

0 

3 

U 

Q) -0.2 

I= -0.4 

- 

- 

- 

-0.6 - 

-0.8 - 

-1.0 - 

-1.2 - Slug Exit Perturbation 

-1.4 I I I I I I I I I I I I 

0123456789101112 

Time (ms) 

Figure 1 1. Measured response function for standard search coil configuration. 

24 
0 Data 

Gaussian Fit 

(o= 1.8 cm) 

1.4 

1.3 

1.2 

1 .I 

- 1.0 z 

5 0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0 

g) 0.9 

+ ca 

> 

0 

- c 

0 1 2 3 4 5 6 7 8 

Distance (cm) 

Figure 12. Gaussian fit of response function for standard search coil configuration. 

25 
250 

200 

150 

n 100 

5 

E 50 

22 

5 

L 

0'0 a 

9 

0 -50 

-1 00 

-1 50 

-200 

-250 

ca 

v) .- 

n 

Pulse Plasma Gun 

27 kV/2 pF 

f=40 kHz 

Figure 13. Measured discharge current waveform for the pulse plasma gun circuit at 27 kV. 

26 
I 

m 

cv 

Figure 14. Ensemble-averaged optical probe waveforms at 25- and 27-inHg vacuum. 

Probes are located at 0, 1,2,3,4, and 5 cm from gun exit. 

27 
5.0- 

4.5 

4.0 

- 3.5 

E 

s 3.0 

- 2.5 

s 

3 2.0- 

2 

1.5 

cn \ 

+ 2-i 

.- 

1 .o 

0.5 

0 

Figure 15. Plasma jet axial velocity distribution at 25- and 27-inHg vacuum. 

Pulse Plasma Gun 

- 27 kVl2 FF 

- 

- 

- 

- 

--

- 

-t- 27-inHg Vacuum (Air) 

__~1__ 25-inHg Vacuum (Air) 

I I I I I I I I I I 

- 

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 

28 
Pulse Plasma Gun 

27 kVl2 pF 

27-inHg Vacuum (Air) 

Figure 16. Measured probe response at 27-inHg vacuum and a discharge voltage of 27 kV. 

29 
REPORT DOCUMENTATION PAGE 

1. AGENCY USE ONLY (Leave Blank) 

Form Approved 

OM8 NO. 0704-0188 

2. REPORT DATE 3. REPORT TYPE AND DATES COVERED 

March 2003 Technical Publication 

I. TITLE AND SUBTITLE 

Magnetic Flux Compression Experiments Using Plasma Armatures 

5. FUNDING NUMBERS 

i. AUTHORS 

M.W. Turner," C.W. Hawk,* and R.J. Litchford 

14. SUBJECT TERMS 

magnetic flux compression, magnetic Reynolds number, interchange 

instability, plasma jet, electrical conductivity, plasmadynamics 

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 

OF REPORT OF THIS PAGE OF ABSTRACT 

Unclassified Unclassified Unclassified 

'. PERFORMING ORGANIZATION NAMES(S) AND ADDRESS(ES) 

15. NUMBER OF PAGES 

40 

16. PRICE CODE 

20. LIMITATION OF ABSTRACT 

Unlimited 

George C. Marshall Space Flight Center 

Marshall Space Flight Center, AL 358 12 

#. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 

National Aeronautics and Space Administration 

Washington, DC 20546-000 1 

8. PERFORMING ORGANIZATION I REPORT NUMBER 

M- 1069 

10. SPONSORINGIMONITORING 

AGENCY REPORT NUMBER 

NASNTP- 2003-2 12341 

I 

11. SUPPLEMENTARY NOTES 

*Propulsion Research Center, The University of Alabama in Huntsville, Huntsville, AL 

Prepared by the Advanced Space Transportation Program Office, Space Transportation Directorate 

l2a. DISTRIBUTION/AVAILABlLlTY STATEMENT 

Unclassified-Unlimi ted 

Subject Category 20 

Standard Distribution 

12b. DISTRIBUTION CODE 

13. ABSTRACT (Maximum 200 words) 

Magnetic flux compression reaction chambers offer considerable promise for controlling the plasma flow associated 

with various micronuclearkhemical pulse propulsion and power schemes, primarily because they avoid 

thermalization with wall structures and permit multicycle operation modes. The major physical effects of concern are 

the diffusion of' magnetic flux into the rapidly expanding plasma cloud and the development of Rayleigh-Taylor 

instabilities at the plasma surface, both of which can severely degrade reactor efficiency and lead to plasma-wall 

impact. A physical parameter of critical importance to these underlying magnetohydrodynamic (MHD) processes is 

the magnetic Reynolds number (R,,,), the value of which depends upon the product of plasma electrical conductivity 

and velocity. Efficient flux compression requires R,,>>I, and a thorough understanding of MHD phenomena at high 

magnetic Reynolds numbers is essential to the reliable design and operation of practical reactors. As a means of 

improving this understanding, a simplified laboratory experiment has been constructed in which the plasma jet 

ejected from an ablative pulse plasma gun is used to investigate plasma armature interaction with magnetic fields. As 

a prelude to intensive study, exploratory experiments were carried out to quantify the magnetic Reynolds number 

characteristics of the plasma jet source. Jet velocity was deduced from time-of-flight measurements using optical 

probes, and electrical conductivity was measured using an inductive probing technique. Using air at 27-inHg 

vacuum, measured velocities approached 4.5 km/s and measured conductivities were in the range of 30 to 40 kS/m. 

I