NASA/TP--2001-210794

Inductive Measurement of Plasma Jet

Electrical Conductivity

(MSFC Center Director's Discretionary Fund Final Report;

Part II, Project No. 99-24)

M. W. Turner and C. W. Hawk

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

January 2001

https://ntrs.nasa.gov/search.jsp?R=20010029205 2018-05-14T14:46:23+00:00Z
Acknowledgments

The authors acknowledge the support of George C. Marshall Space Flight Center (MSFC), National Aeronautics and

Space Administration (NASA). This Technical Publication represents the Final Report (Part II) for MSFC Center Director's

Discretionary Fund (CDDF) Project No. 99-24. The NASA Prinicipal Investigator was Ron J. Litchford, TDI5/ASTP.

This Technical Publication has been reviewed and is approved.

Garry M. Lyles

Manager

TD15/ASTP

Marshall Space Flight Center

Available from:

NASA Center for AeroSpace Information

712 ! Standard Drive

Hanover, MD 21076-1320

(301) 621-0390

National Technical Information Scrvice

5285 Port Royal Road

Springfield, VA 22161

(703) 487-4650

ii
TABLE OF CONTENTS

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

2. MAGNETIC DIFFUSION PHENOMENA ....................................................................................

3. THEORY OF INDUCTIVE PROBE ..............................................................................................

3.1 Fundamental Principles of Operation ......................................................................................

3.2 Mathematical Theory of Operation ..........................................................................................

4. PROBE DEVELOPMENT .............................................................................................................

4.1 Design ......................................................................................................................................

4.2 Calibration ................................................................................................................................

5. PLASMA JET EXPERIMENTS ....................................................................................................

6. CONCLUSIONS .............................................................................................................................

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

1

5

7

7

8

11

11

13

17

23

25

..°

111

.

.

3.

.

5.

6.

7.

.

,

10.

11.

12.

13.

14.

LIST OF FIGURES

Mark I configuration for an explosively driven radial-mode magnetic flux

compression reactor. This device is intended to serve as a moderate-scale

technology demonstrator as well as a low-cost expendable unit for supporting

basic research ........................................................................................................................

Illustration of plasma jet collisional process and radial armature formation .......................

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

the field lines of the excitation coil and induces an emf 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 (Rd) is 1 kf2 ...........................................................................................

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 .................................................................

Time-of-flight waveforms from calibration experiments. Statistical parameters

are indicated. Mean value-/,t; standard deviation--o .............................................................

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

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

Measured response function for push-pull search coil configuration ...................................

Validation calculations for constrained linear inversion technique ......................................

Photograph of cast octol shaped charges with 0-, 1-, and 2-percent potassium carbonate

seed by mass .........................................................................................................................

2

3

7

8

11

12

12

13

14

14

15

16

16

17
15.

16.

17.

18.

19.

20.

LIST OF FIGURES (Continued)

Schematic of expendable explosive units for measuring plasma jet

electrical conductivity ...........................................................................................................

Photograph of assembled explosive unit in blast chamber with attached detonator ............

Representative time-of-flight waveform for typical explosive plasma jet ............................

Representative push-pull pickup coil waveforms for typical unseeded explosive

plasma jet ..............................................................................................................................

Representative push-pull pickup coil waveforms for typical seeded explosive

plasma jet ..............................................................................................................................

Gaussian fit to entrance perturbation signal for unseeded and seeded charges ....................

18

18

19

20

20

21

l,

2.

LIST OF TABLES

Summary of plasma jet measurements based on the peak ratio method ..............................

Summary of plasma jet measurements based on the integral ratio method ..........................

22

22

vi
LIST OF ACRONYMS AND SYMBOLS

AI

C4

emf

He

HEDM

MHD

TP

aluminum

composition-4

electromotive force

helium

high-energy density matter

magnetohydrodynamic

technical publication

vii
NOMENCLATURE

0

B app

Bind

Om

f

f(¢)

g

g(s)

H

I

I

I c

lsp

K

K r

K(s,¢)

l

L

Lo

R

Rd

R m

s

t

appropriate characteristic value for the problem (subscript)

applied magnetic induction

induced magnetic induction

magnetic diffusivity

mx I column matrix

distribution function

nx 1 column matrix

measured signal

constraint matrix

identify matrix

field coil current during a test

field coil current during calibration

specific impulse

nxm kernel matrix

transpose of K

kernel

length of the conductive region behind the shock

inductance

characteristic length of the reactor

resistance

damping resistance

magnetic Reynolds number

distance from the search coil to the shock

time

VIII
U

U 0

U c

U

V(s)

X

C

'_i

11

_=-S--X

P

(Y

(7

%

_(s)

_c

_z

NOMENCLATURE (Continued)

particle velocity behind the shock

characteristic plasma velocity

velocity of the calibration slug

velocity of the shock

calibration response function or kernel

peak value of calibration slug response

peak value of the calculated voltage curve

output signal of the search coil

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

differential change

smoothing parameter

finite measurement error

ith eigenvalue of the covariance matrix

magnetic permeability

distance from an arbitrary location x to the shock

resistivity

electrical conductivity

maximum conductivity

characteristic plasma electrical conductivity

calibration slug conductivity

pulse area of measured voltage curve

integrated-induced voltage signal

pulse area of calibration slug response function

function dependent on the conductivity distribution

function dependent on the conductivity distribution

ix

TECHNICAL PUBLICATION

INDUCTIVE MEASUREMENT OF PLASMA JET ELECTRICAL CONDUCTIVITY

(MSFC Center Director's Discretionary Fund Final Report; Part II, Project No. 99-24)

1. INTRODUCTION

The need for fast, efficient interplanetary transport has led to the serious consideration of various

concepts for nuclear/chemical pulsed propulsion and power. It is believed, for instance, that propulsion

systems of this type are within the grasp of modern technical capability and can eventually yield the rapid

acceleration and high specific impulse (Isp) attributes that are deemed necessary. Actual success, of course,

will depend upon the ability to overcome practical technical issues. For example, these concepts rest on the

assumption that low-yield microfusion/fission detonations or chemical detonations using high-energy density

matter (HEDM) can eventually be realized in practice and that enabling technologies such as high-power

standoff drivers and simple, effective reactor designs can be developed.

The simplest reactor design for propulsion is a pusher plate that physically interacts with the blast

wave from the detonation. However, more intricate reactor schemes can be conceived in which the expanding

diamagnetic plasma is forced to interact with an applied magnetic field. 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.

Specific pulsed magnetic flux compression reactor concepts are, in fact, currently being considered

for spacecraft propulsion and power. 1 In these devices, the expanding diamagnetic plasma cloud compresses

the initial magnetic flux within a semi-enclosed reactor structure until the expansion is ultimately reversed

by increasing magnetic pressure. The detonation products are then collimated and expelled, and electrical

power can be inductively extracted.

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

compression reactors is the magnetic Reynolds number (Rm), 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 m >> 1. As such, a thorough understanding of MHD phenomena at high R m is essential to the

design of flux compression reactors as well as explosively driven MHD converters.

Explosive sources offer a simple and convenient method for producing high-speed, highly conductive

plasma jets, and it is contended that these sources represent a path for conducting meaningful nonnuclear

demonstration tests. The Mark I device envisioned by Litchford et al., for instance, is shown schematically

in figure I. J This is a radial-mode flux compression reactor which uses colliding plasma jets from opposing

high-explosive charges to produce a radially expanding plasma armature. The plasma armature is then used

to compress a trapped magnetic field against a conductive stator surface. The Mark I configuration is

intended to serve as a moderate scale (l/2-m-diameter) technology demonstrator as well as a low-cost

expendable unit for supporting basic scientific investigations.
Shielding Shell Magnetic Coil

Generator Coil Plasma Armature

_Shaped Charge

I Explosive

Figure 1. Mark I configuration for an explosively driven radial-mode

magnetic flux compression reactor.l This device is intended

to serve as a moderate-scale technology demonstrator as well

as a low-cost expendable unit for supporting basic research.

As a step toward realizing this device, an effort has been initiated to explore the utilization of

explosively driven plasma sources for compression of magnetic fields and to quantify achievable magnetic

Reynolds number. Available empirical data for the electrical conductivity of explosive plasma jets are

limited, but there is evidence to indicate that sufficiently high R m can be produced.

For instance, experiments on 44 ° cavity charges of composition-4 (C4) by Burnham and Marshall

have revealed that a cohesive plasma slug is ejected at speeds on the order of 3× 104 m/sec with a core

electrical conductivity of 10 4 S/m. 2--4 Collisional processes between colliding jets, as illustrated in figure

2, were also observed through high-speed photography. Independent explosive-driven MHD experiments

by Jones and McKinnon indicated the production of R m approaching unity in moderate-scale devices. 5

Explosive plasma sources developed by Baum and Shimmin have produced plasma flow velocities of

30 km/sec and conductivities of 30 kS/m, which in a laboratory-scale, 25-mm-diameter tube yields an R m

of 28. 6 The explosive compressor developed by Voitenko produces comparable shock velocities and is

likely to have a comparable range of Rm .7 Furthermore, a concept for explosive-driven collapse of a lined

cylindrical cavity, as proposed by Koski et al., has shown considerable promise as well. 8-1°

2
PrecursorIonization

'_- RadiallyExpanding

PlasmaArmature

Figure 2. Illustration of plasma jet collisional process and radial armature formation.

Based on this evidence, research had proceeded with the development of a simple and reliable

inductive probe for measuring the electrical conductivity of explosive plasma jets. A more direct approach

using biased contact electrodes is possible, but it is well known that this methodology suffers from large

surface resistances, and an electrodeless technique is preferred. Therefore, it was decided to adapt the

inductive probing technique developed by Lin, Resler, and Kantrowitz for shock tube studies.ll In this

method, the perturbation of an applied magnetic field by a plasma jet induces a voltage in a search coil,

which, in turn, can be used to infer electrical conductivity through the inversion of a Fredholm integral

equation of the first kind. This technical publication (TP) describes the design, development, and calibration

of a 1-in.-diameter probe and the results of exploratory experiments using plasma jets expelled from 15-g

shaped charges formed from seeded and unseeded octol.

2. MAGNETIC DIFFUSION PHENOMENA

Some of the major plasmadynamic issues associated with detonation plasma-driven field compression

are as follows: (1) Achieving sufficiently high expansion velocity and electrical conductivity to ensure

diamagnetic behavior, (2) electron Joule heating effects, (3) field-aligned ion flow due to the ambipolar

potential, (4) Rayleigh-Taylor surface instabilities, and (5) ensuring rebound of the plasma expansion. In

this TE the effects of magnetic diffusion, particularly with respect to explosively generated plasma sources,

are of primary concern.

There are a number of alternative ways to visualize the interaction between a moving conductor

and a magnetic field. Perhaps the most common means of describing the phenomena is in terms of distortion

of magnetic field lines by the conductor entering the field region and subsequent diffusion of field lines

into the conductor. For a finite electrical conductivity (cy), the field lines diffuse into the conductor at a rate

governed by the magnetic diffusivity (Dm = 1/_o') where _ is the magnetic permeability.

The diamagnetic properties of plasma jets can be quantitatively measured by the relative value of

the magnetic Reynolds number, a parameter that naturally evolves from dimensional analysis of the MHD

equations in the form

Rm - Bind - 130_ouoLo , ( 1)

Bapp

where 0 subscript denotes an appropriate characteristic value for the problem. Here, c_0 is the characteristic

plasma electrical conductivity, u 0 is the characteristic plasma velocity, and L0 is a characteristic length of

the reactor (e.g., diameter). In a general sense, R m may be thought of as a relative measure of the induced

magnetic induction in the plasma (Bind) with respect to the external applied magnetic induction (Bapp).

According to the definition of magnetic diffusivity, it is inferred that the magnetic Reynolds number is

inversely related to the magnetic diffusivity (Din):

u0Lo (2)

gt_l =-

Dm

The interaction between a moving conductor and a magnetic field may also be described in terms of

eddy currents produced by gradients in the Faraday voltage. From this perspective, the eddy currents induce

a perturbation field which, when added to the original field, distorts the field lines. The strength of the eddy

current loops depends on the ratio of Faraday voltage to loop resistance, which may be shown to be

proportional to R m. Growth and decay of the eddy current loops are determined by the inductive L/R decay

time of the current loop, which is directly related to the diffusion time.

Thus, it is clear that for magnetic Reynolds numbers greater than unity, where the induced field is at

least as strong as the applied field, the plasma will be resistive to magnetic diffusion. That is, the induced
field associated with eddy currents in the plasma act in an opposing direction to the applied field, and if the

induced field is high enough, the plasma interface effectively behaves as a magnetic compression surface.

The important point to note is that R m depends primarily on the product ou such that one would

desire high electrical conductivity and high expansion velocities in order to achieve low-flux diffusion

losses. For nuclear detonations, both of these parameters are extremely high and R m >>1, as desired. For

conventional chemical detonations, the characteristic values are marginal and the plasma jet sources must

be carefully designed to achieve R m > 1.

6
3. THEORY OF INDUCTIVE PROBE

3.1 Fundamental Principles of Operation

The inductive probe, illustrated in figure 3, 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 the dc power

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

illustrated in figure 3. 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.

Plasma Jet

Lin Coil

System

Field Lines

Evacuated J

Shock Tube

Search Coil Field Coil

Figure 3. Illustration of inductive probe principle of operation. The

plasma jet displaces the field lines of the excitation coil

and induces an emf in the search coil. The degree of field

displacement can be correlated with plasma jet electrical

conductivity.

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 the following subsection 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 device. ] I
3.2 Mathematical Theory of Operation

Following the mathematical analysis of Lin et al. for the inductive probe, a Fredholm integral

equation of the first kind for the conductivity cr is arrived at: 11

,I,(s)= Uu/ .c vcIs- ¢)o(¢) (3)

where _(s) is the integrated-induced voltage signal on the search coil

O(s) = ;0 V(s) ds , (4)

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 4. The major parameters are as follows: Length of the conductive region behind

the shock (1), distance from the search coil to the shock (s), distance from the search coil to an arbitrary

point behind the shock (x), distance from an arbitrary location x to the shock (_=s-x), velocity of the shock

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

(uc), field current during calibration (It), electrical conductivity of the calibration slug (o'c), calibration

response function or kernel (Vc), and the unknown plasma electrical conductivity distribution (or).

_, i ...... J :

S

ShockFront

u

SearchCoil FieldCoil

Figure 4. Diagram of parameters relevant to the mathematical

analysis of probe operation.
TheFredholmintegralequationof thefirst kind hasthegeneralform

b

g(s)--f.a dg , (5)

where g(s) is a known function (i.e., the measured signal), K(s,_) is the kernel, andf(_) 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.

Deconvolution algorithms for recovering f(_) are generally based on a linear vector space

representation in the form

g(si)=ZK(si,_j)f(_j) , (6)

which may be written in matrix form as

g = Kf , (7)

where g is an n×l column matrix, fis an m×! column matrix, and K is an n×m matrix, which may include

numerical quadrature coefficients. Multiplying through by K T and inverting yields the desired distribution

function

f = (KTK) -1 .KT.g (8)

Unfortunately, this least-squares linear inversion is subject to instability because of the ill-conditioned

kernel and because the kernel may exhibit linear dependence. Given a finite measurement error (e), Twomey

showed that the resulting error in f would be 12

(9)

where "_iis the ith eigenvalue of the covariance matrix defined by the product KK T. For relatively large offdiagonal terms, the eigenvalues can be extremely small and a finite measurement error _ can lead to a large

error in f.

A simple modification to least-squares linear inversion, known as constrained linear inversion, can

sometimes avoid the severe instabilities and permit a reasonably accurate numerical inversion. A description

of constrained linear inversion is given by Twomey. 12 Following Twomey's development, the following is

obtained:

f= KTK+yH )-1 •KT .g , (10)
whereaconstraintmatrixH along with a Lagrange multiplier y has been introduced, such that

O_<y<oo (11)

It is easy to see that when y=0, there is no smoothing and the least-squares linear inversion is recovered.

When y---) oo, infinite smoothness is approached, such that all information is smeared away. As such, the

desire is to have y be as small as possible while also maintaining numerical stability. H can have different

forms, depending on how one defines the smoothness. Using sum of squares as a smoothness indicator, H

becomes the identity matrix

H=I (12)

In some cases, 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 (o'*) behind the shock wave and the calibration slug conductivity (orc ) as

,r*_ ,,,,IcVp

crc UulVcp

_1 (13)

or

a* u2 lc_

crc Uul_ c

II/2 , (14)

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

and • are the peak and the pulse area of the measured voltage curve, and VI and V2 are functions dependent

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

literature. 1 1

For the special case where the conductivity distribution is a step function and the probe response

function is Gaussian, both qtI and V2 are unity. When the conductivity distribution deviates from a step

function, both V1 and V2 can become complicated functions that may only be evaluated numerically. At

any rate, it should be pointed out that when the variation of conducting is not too great, V2 will be unity

plus a small correction term. This behavior turns out to be quite fortuitous for the purpose of analyzing the

plasma jets encountered in our experiments.

10
4. PROBE DEVELOPMENT

4.1 Design

The detailed design of the inductive probe is shown in figure 5. The basic structure is a nylon coil

form that has been machined to accept two coil windings. The coil form has a bore diameter of 1.3 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 1.5 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

push-pull configuration as discussed below.

AllMeasurementsin Inches

Material:Nylon

_1.425

_---- 1.5-_-_ 0.125--.-t .-_ '*-0.125

Figure 5. Detailed design drawing of probe.

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 sec 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 6. A rise time of 20 msec, a peak current of

56 A, and a peak field intensity of 0.8 T was observed. Reproducibility of these waveforms was excellent.

The waveforms remain relatively flat around the peak values for =15 msec after which they gradually

decay and stabilize to =63 percent of their maximum values. Therefore, a 15-msec target window in which

to probe the plasma jet at maximum field strength was available.

11
60

50

v 40

=_ 30

.__

_ 2o

10

I I

Current(A) I.......... I

....... Magnetic Field(1_ i _ -

• I I

s_ N_

/

/4 Window

., f

p

, /

)

_j

,,/

,i

7

it

7

ILll/_lLIL|LLIr

0 10

i i i i I i ,[L , I , , ,

0

-10 20 30 40

Time (msec)

1

0.9

•0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

' 0

50

z

c,J

Figure 6. Measured coil current and field intensity waveforms.

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

associated with nonuniform charge distributions in the ionized gas. I i 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 7. The center tap is connected to ground and 1 kf_ 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 the probe design so that either a

50-turn standard connection or a dual 25-turn push-pull connection could be utilized, as needed.

i..---- L ----_

,/. Z-V <_ -

t 7,f: '4

I I

I !l q ii

I llll ;ll',l II I

t li II ;I I I Vi'

!

I L_______ _/

7

D

J

Itt

L_- t

f_

I

i I D

I i .. ,

L ii I s. •

____J

Standard Configuration Push-Pull Configuration

Figure 7. Illustration of standard and push-pull search coil configurations.

The critical damping resistance (Rd) is 1 kf_.

12
4.2 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

requirement, a simple compressed gas gun using 150 lb/in 2 helium (He) stored in a small cylinder was

developed. 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 (A1) cylinder was propelled down a

plastic barrel and through a glass tube holding the probe assembly. The resistivity of the aluminum was

p= 3 x 10 -8 f_.m. The velocity of the slug was inferred from the deflection of a laser beam. A digital computercontrolled firing sequence was implemented incorporating appropriate timing delays, and the various signal

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

figure 8.

Pressure- ManualValve

Regulated -F

Helium-D,.-----.I:>I<3_

I Compressed GasCylinder

Pressure

-_ LinCoil

Gauge Laser

PlasticBarrel System

_ Brlech _ [L-_

Solenoid 0 )tical

Actuated Detector

Valve

GlassTube

Section

GuideTube

,5

Figure 8. 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.

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

necessary to accurately trigger the excitation field coil 20 msec betore the slug entered the active probe

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

timing problem was summarily resolved after several test shots.

To measure the slug velocity, a laser beam was directed 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, the time of flight of the slug past the beam could be determined and the velocity

inferred from the known slug length. The captured detector waveforms are shown in figure 9 from which a

time of flight of At=5 msec was observed. A slug velocity of 2150_+ 164 cm/sec was deduced.

13
14

12

10

0

-I0

8

¢0

¢I,

0

6t

/.t: 4.75 msec

_: 363 lasec

-5

f A_

Uc

2,t50 cm/sec

164 cm/sec

J i I J E i i J J i i i

0 5 10

Time (msec)

Figure 9. Time-of-flight waveforms from calibration experiments.

Statistical parameters are indicated. Mean value-p;

standard deviation-or.

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

figure 10. 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.

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0

-0.2

-0.4

-0.6

-0.8

-1.0

-1.2

-1.4

0

A

>_..

_E

_ Slug EntrancePerturbation

] \ Calibration Response Function

] \ Seven-Waveform EnsembleAverage

] \ Standard Configuration

t \ Lc=lO2cm

[ \ ,Uc= 2,150 + 164 cm/sec

.} _0) -8 _-m

J I J I _ I L I _ I J i _ 1 _ 1 J I J I L i ,

1 2 3 4 5 6 7 8 9 10 11 12

Time (msec)

Figure 10. Measured response function for standard search coil configuration.

14
1.4

1.3

1.2

1.1

1.0

0.9

0.8

_" 0.7

_ 0.6

"_ 0.5

0.4

0.3

0,2

0,1

0

0

0 Data

-- Gaussian Fit

(c= 1.8 cm)

?L _kI h _ I I L ,I ,I , , I , ,,,_c._, ,

1 2 3 4 5 6 7 8

I]islance (cm)

Figure 11. Gaussian fit of response function for standard search

coil configuration.

The response function is nearly Gaussian as can be seen from the fit shown in figure !1. Here,

transformation is made to spatial coordinates using the known slug velocity. The response function is

observed to reach 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.

The measured response functions for the push-pull search coil configuration (25-turn segments) is

shown in figure 12. Again, these waveforms represent an ensemble average of seven independent shots. In

this case, a response signal was obtained Irom each segment of the push-pull 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.

For the purpose of performing numerical inversions of the integral equation, Gaussian fits for the

response function are always utilized. Use of experimental data points introduces unnecessary complexity

and can even lead to numerical inaccuracies. This method is followed for both standard and push-pull

configurations.

At this stage, a code for the constrained linear inversion technique was implemented and a validation

calculation. The general approach was to use the aluminum slug response function in conjunction with a

simulated Gaussian signal to test the algorithm. The simulated Gaussian signal was integrated to obtain

• (s) and inversions were attempted in which H = I and the smoothing parameter (y) was varied over a wide

range of values. In theory, a Gaussian response signal should deconvolve to a step function. The result of

our inversion code is shown in figure 13 using 7= 10-3.

15
Figure 12.

0.5

;9 0

I

-0.5

-- Push

.... Pull

A

Calibration Response Function

Seven-Waveform Ensemble Average

Push-Pull Configuration

t"" Lc = 10.2 cm

t _ Pc= 2,150_+ 164 cm/sec

t xPc= 3(10) -8 _-m

!

Slug Entrance Perturbation Slug Exit Perturbation

-1 J I J I , I _ I _ I , I , i , i , i , i j I i I

0 1 2 3 4 5 6 7 8 9 10 11 12

Time (msec)

Measured response function for push-pull search coil configuration.

Figure 13.

1.4

1.3

1.2 -

1.1 -

1.0-

0.9-

0.8-

0.7 -

0.6 r

0,5 -

0.4-

0.3-

0.2-

0,1

0

Constrained Linear Inversion

(H = I ; ? = 10-3)

Exact

0 1

L,I,iiIi

2 3

Distance (cm)

i

, J I L , _ I r _ P

4 5

Validation calculations for constrained linear inversion technique.

The result is clearly not pleasing due to the overshoots and ringing errors, but the algorithm does

produce a rough approximation. The Lagrange multiplier is close to zero but more smoothing is needed.

Unfortunately, increasing the value of 7 results in poorer performance. Additional modifications will be

required to make this deconvolution algorithm sufficiently robust for reliable use.

16
5. PLASMA JET EXPERIMENTS

With probe development completed, exploratory laboratory experiments on explosive plasma jets

were initiated. In these experiments, 15-g shaped charges (included cone angle of 44 °) composed of octol

(75 percent HMX/25 percent TNT) with various amounts of seed material (0-, 1-, and 2-percent potassium

carbonate by mass) were investigated. Sample cast charges are shown photographically in figure 14. Note

the change in colorization with seed fraction. All charges were prepared by Accurate Arms Company,

McEwen, TN. Based on previous experiments with similar explosives, plasma jet velocities around 10 kin/

sec and electrical conductivities in the 10 kS/m range were anticipated.

Figure 14. Photograph of cast octol shaped charges with 0-, 1-,

and 2-percent potassium carbonate seed by mass.

The simple experimental setup is illustrated in figure 15. Here, a shaped charge explosive is attached

to a schedule 40 PVC pipe that includes a time-of-flight circuit and an inductive probe. The overall length

of these expendable units was 40 in., and end caps were attached so that a rough vacuum in the pipe prior

to a test could be established. The time-of-flight circuit consisted of two wires traversing the pipe with a

separation distance of 10 cm. The first wire was located 8.5 in. from the shaped charge exit plane. A dc

voltage (24 V) was applied to these wires, and the cun'ent was measured across appropriately sized ballast

resistors. When the plasma jet broke each wire, the respective current signals would fall such that the time

of flight between the two locations could be measured. A time of flight of 10 _sec for an estimated jet

velocity of 10 kin/see was anticipated.

Expendable coil forms were fi_bricated and motmted to the PVC pipe and field coils and search

coils were wound on these forms. The dimensions o.f these expendable probes were identical to those used

in O__lrcaliN-_t!i_m ,,york. The prol>.:s w¢::'re l{_ca!ed 15 i,._.,flom the shaped charge exit plane.

17
Time-of-Flight

Circuit Lin Coil

Cavity _ I System /

Charge---_

EvacuatedTube

\

--- = k_ Field Coil

SearchCoil

Figure 15. Schematic of expendable explosive units for measuring

plasma jet electrical conductivity.

The tests were conducted in a blast chamber located at Accurate Arms Company test facilities in

Bucksnort, TN. To conduct a test, the assembled explosive units were placed in the chamber and a 200-

msec delay initiator was attached to the end of the shaped charges as shown in figure 16. The delay initiator

was necessary to ensure that the plasma jet passed through the probe during the desired target window at

maximum field coil strength. It took slightly less than 200 msec for the solenoid-controlled relay to close.

A rough vacuum would be established in the pipe, and a dual-circuit switch would be activated to excite the

field coil and initiate the explosion. Data from the experiment were captured on a four-channel digital

oscilloscope.

Figure 16. Photograph of assembled explosive unit in blast

chamber with attached detonator.

18
Representative time-of-flight waveforms from a typical test are shown in figure 17. The letter A

denotes the first trip wire and letter B denotes the second trip wire. In this particular test without seed, the

time of flight was 11 psec, yielding a jet velocity of 9.1 km/sec, which is very near the anticipated value of

10 km/sec. The measured velocity invariably ranged between 9 and 10 km/sec with no dependence on

seeding. The average time of flight from all usable test results was 11.2 ,usec, yielding an average velocity

of 9 km/sec.

To avoid any possible electrostatic effects on the probe measurements, the push-pull search coil

configuration for all tests was utilized. Representative waveforms from a typical test are shown in figure

18. In this test, there was no seed in the charge, and the entire response occurred within 30/_sec. The peak

signal amplitude is =22 V, and the push-pull signals are symmetric, as expected. The signal oscillations

appear to be indicative of tears in the plasma jet due to a strong axial gradient in velocity. This result could

be anticipated from the work of previous researchers in the field.

Waveforms obtained using seeded shaped charges were similar except the peak signal amplitudes

ranged from 90 to 100 V. Representative push-pull pickup coil waveforms for a typical seeded explosive

plasma jet are shown in figure 19. The increased peak voltage indicated a substantial increase in electrical

conductivity, as expected.

In all cases, the entrance perturbation closely resembled a Gaussian response, indicating an abrupt

and very strong increase in ionization behind the shock front. Attempts to perform Gaussian fits on the

entrance perturbations for cases with and without seed arc shown in figure 20. It is clear that the rising edge

is more nearly Gaussian while the falling edge is extremely abrupt. However, the Gaussian does tend to fit

slightly beyond the peak amplitude in all cases.

30

A

25

5

0

0

20

15

o_

"" 10

Figure 17.

Tests2-7 (0%Seed)

10 20 30 40 50

Time(psec)

Representative time-of-flight waveform

for typical explosive plasma jet.

19
25

2O

Push Coil Tests 2-10 (0% Seed)

15

10

-20

Pull Coil

-25

0 10 20 30 40 50

Time (psec)

Figure 18. Representative push-pull pickup coil waveforms for typical

unseeded explosive plasma jet.

100

75

Push Coil Tests 2-12 (2% Seed)

5O

-75

Pull Coil

-1 O00 10 20 30 40 bO

Time (iJsec)

Figure 19. Representative push-pull pickup coil waveforms

for typical seeded explosive plasma jet.

2O
22

20

18

o

=-12

" 10

._ 8

6

4

2

0

Tests 2-10 (0% Seed) 110

Data _ 100

90

8o

7O

o

_- 60

" 50

_ 4o

a.

3O

2O

10

',! I . , I I |1 , I

1 2 3 4 5 O0

s(cm)

Tests 2-12 2% Seed)

-- Data

, I

1 2 3 4 5

s(cm)

10 t- Tests 2-4 (0% Seed) 110

9 _ Data . . e'_ 100

B _ 90

7 =80

== 6 ==_70

_ 60

_. 5 =

"" 50

2 4 _ 40

" 3 "30

2 20

1 10

O0 1 2 3 4 ,, 5I O0

s(cm)

Tests 2-6 (2% Seed)

-- Data

o GaussianFit

I

1 2 3 4 5

s(cm)

Figure 20. Gaussian fit to entrance perturbation signal for unseeded and seeded charges.

The results of four tests are summarized in tables I and 2 based on peak ratio and peak integral

methods. Two are without seed and two are with seed. The measured jet velocities are also shown. Assuming

that the entrance perturbations can be reasonably approximated by a Gaussian, peak electrical conductivity

values in the plasma jet are inferred, using eq. (13), where it is implicitly assumed that 9rj is approximately

unity. The results for the integral ratio method are based on eq. (14) with gt2 taken as unity. In general, the

integral ratio method is a better approximation since q/2 exhibits less deviation from unity in all cases.

The peak electrical conductivity was found to be in the range of 4 kS/m for unseeded charges and in

the range of 20 kS/m for seeded charges. Using the measured jet velocity, it was estimated that the product

t.tcy*u may be as high as 46 m -] for unseeded charges and 228 m I for seeded charges. This implies that

significantly high values for the R m in moderate-scale devices can be achieved; that is, devices which are

measured in fractions of a meter. This implies that seeded shaped charges may be adequate for the proposed

Mark I demonstration device.

21
Table l,

Parameter

Seeding

U

o-*/_ c

c* U/CcUc

(3,

HO'* U

Summary of plasma jet measurements based

on the peak ratio method.

Dimension

%

km/sec

10-5

10-2

kS/m

m-1

Peak RatioMethod (_1=1)

2-4 2-10

0 0

9.1 10

7.8 14

3.3 6.5

2.6 4.6

29 58

2-6 2-12

2 2

9.5 9.1

76 78

34 33

25 26

300 295

Table 2. Summary of plasma jet measurements based

on the integral ratio method.

Parameter

Seeding

L/

*u/_c uc

G*

pO'* U

Dimension

%

km/sec

10-5

10-2

kS/m

m-1

Integral RatioMethod (_2=1)

2-4

0

9.1

5.9

2,5

1.9

22

2-10 2-6 2-12

0

10

11

53

3.6

46

2

9,5

58

26

19

228

2

9.1

56

24

18

210

22
6. CONCLUSIONS

An electrodeless inductive probe for measuring plasma jet electrical conductivity was designed,

fabricated, calibrated, and tested. The 1-in.-diameter probe uses an excitation solenoid coil to produce an

axisymmetric field within the bore, and a search coil is located nearby to detect field perturbations when

the plasma jet enters the active probing region. The response function for the probe was obtained through

a calibration procedure in which a metal slug of known conductivity was propelled through the probe with

a known velocity. The signal obtained for an actual plasma jet experiment could then be used to determine

conductivity through the inversion of a Fredholm integral equation of the first kind. A constrained linear

inversion algorithm was developed for this purpose, but the results were only marginally successful. A

more practical approach is to assume a conductivity distribution for which approximate analytical solutions

are known.

Exploratory laboratory experiments were conducted using seeded and unseeded shaped charge

explosives. The jet velocity was inferred from time-of-flight measurements and electrical conductivity

determined from measurements using the inductive probe. The average jet velocity was =9 km/sec and the

measured conductivities were in the range of 4 kS/m for unseeded charges and in the range of 26 kS/m for

seeded charges. These values imply that seeded shaped charge explosive plasma jets can achieve magnetic

Reynolds numbers significantly higher than unity in a moderate-scale device. This indicates that the proposed

Mark I device built on a scale of fractions of a meter has a good chance of being successfully developed.

It is concluded that an inductive probing technique represents a very useful and reliable tool for

investigating plasma jet ionization characteristics. Based on the results obtained in our exploratory

experiments, it is further concluded that high-explosive plasma sources are capable of producing very high

magnetic Reynolds number jets that can be of significant use in the development of magnetic flux

compression reactors for pulsed nuclear/chemical propulsion and power. Additional experimental studies

along these lines are recommended.

23

REFERENCES

1. Litchford, R.J.; Robertson, G.A.; Hawk, C.W.; Turner, M.W.: and Koelfgen, S.: "Magnetic Flux

Compression Reactor Concepts for Spacecraft Propulsion and Power," AIAA Paper 2000-2669, 2000.

. Burnham, M.W.; and Marshall, S.J.:"Some Experiments Related to Explosive Driven MHD Converters,"

First Conference ol7 Megagauss Magnetic: Field Generation by Explosives and Related Experiments,

Frascati, Italy, H. Knoepfel and F. Herlach (eds.), Euratom publication EUR 2750.e, pp. 367-386,

1966.

. Burnham, M.W.: "Explosive Parameters for Magnetohydrodynamic Energy Conversion," Aeronautical

Systems Division, Air Force Systems Command, Eglin Air Force Base, Final Report ASD-TDR-63-

37, Prepared by Falcon Research and Development Co. under contract No. AF 08(635)-2918, Sept.

1963.

4. Burnham, M.W.; and Marshall, S.J.: "Pulsed Electrical Power from Conventional Explosives," Proc.

of lnt. Symposium on MHD Electrical Power Generation, Paris, France, pp. 753-764, July 1964.

.

Jones, M.S.; and McKinnon, C.N.: "Explosive Driven Linear MHD Generators," First Conference on

Megagauss Magnetic Field Generation by Explosives and Related Experiments, Frascati, Italy,

H. Knoepfe] and E Herlach (eds.), Euratom publication EUR 2750.e, pp. 349-366, 1966.

. Baum, D.W.; and Shimmin, W.L.: "Explosive Plasma Source Experiment," Second bit. Conf on

Megagauss Magnetic Field Generation and Related Topics, Washington, DC, P.J. Turchi (ed.),

Megagauss Physics and Technology, Plenum Press, New York, pp. 77-88, 1980.

7. Voitenko, A.E.: "Generation of High-Speed Gas Jets," Soviet Phys.--Doklady, Vol. 9, No. 10, pp. 860-

862, 1965.

8. Koski, W.S.; Lucy, EA.; Shreffier, R.G.; and Willig, F.J.: "Fast Jets and Collapsing Cylinders," J. App.

Phys., Vol. 23, No. 12, pp. 1300-1305, 1952.

9. Wild, J.M.: "The Production of High-Velocity, High-Density Plasmas With Explosives," General

Atomics Report GA-2401, July 1961.

10. Dunne, B.B.; Blackstead, A.W.; McKinney, W.B.; and Ritter, P.B.: "Mass of High Velocity Gases

From Toroidal Implosion Charges," General Atomics Report GAMD-3629, Oct. 1962.

11. 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, 1987.

12. Twomey, S.: Introduction to the Mathematics of lnversion in Remote Sensing and Indirect Measurements,

American Elsevier, New York, 1977.

25
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January 2001 Technical Publication

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

Inductive Measurement of Plasma Jet Electrical Conductivity

(MSFC Center Director's Discretionary Fund Final Report;

Part II, Project No. 99-24)

6, AUTHORS

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

7. PERFORMINGORGANIZATIONNAMES(S) ANDADDRESS(ES)

George C. Marshall Space Flight Center

Marshall Space Flight Center, AL 35812

9. SPONSORING/MONITORING AGENCYNAME(S)ANDADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

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M-996

IO. SPONSORING/MONITORING

AGENCY REPORTNUMSER

NASA/TP--2001-210794

Prepared by the Advanced Space Transportation Program, Space Transportation Directorate

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

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13. ABSTRACT (Maximum 200 words)

Measurement of plasma jet electrical conductivity has utility in the development of explosively driven

magnetohydrodynamic (MHD) energy converters as well as magnetic flux compression reaction chambers for

nuclear/chemical pulse propulsion and power. Within these types of reactors, the physical parameter of critical

importance to underlying MHD processes is the magnetic Reynolds number, the value of which depends upon the

product of plasma electrical conductivity and velocity. Therefore, a thorough understanding of MHD phenomena at

high magnetic Reynolds number is essential, and methods are needed for the accurate and reliable measurement of

electrical conductivity in high-speed plasma jets. It is well known that direct measurements using electrodes suffer

from large surface resistances, and an electrodeless technique is desired. To address this need, an inductive probing

scheme, originally developed for shock tube studies, has been adapted. In this method, the perturbation of an applied

magnetic field by a plasma jet induces a voltage in a search coil, which, in turn, can be used to infer electrical

conductivity through the inversion of a Fredholm integral equation of the first kind. A l-in.-diameter probe was

designed and constructed, and calibration was accomplished by firing an aluminum slug through the probe using a

light-gas gun. Exploratory laboratory experiments were carried out using plasma jets expelled from 15-g shaped

charges. Measured conductivities were in the range of 4 kS/m for unseeded octol charges and 26 kS/m for seeded

octol charges containing 2-percent potassium carbonate by mass.

14. SUBJECT TERMS

plasmadynamics, plasma jet, electrical conductivity, experimental, high

explosive, shaped charge, magnetic Reynolds number, electromagnetics

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