Magnetic Flux Compression Reactor Concepts for Spacecraft ...

NASA

/ Tpi2001-210793

Magnetic

Flux Compression

Concepts for Spacecraft and Power (MSFC

Center

Part I, Project R.J. Litchford Marshall

C.W.

January

Flight

M.W.

Discretionary

Fund

Robertson Center,

Tumer,

of Alabama

2001

Propulsion

No. 99-24)

and G.A.

Space

Hawk,

University

Director's

Reactor

Marshall

Space

Flight

Center,

and S. Koelfgen

in Huntsville,

Huntsville,

Alabama

Alabama

Final

Report;

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Information

NASA

/ TP--2001-210793

Magnetic Flux Compression Reactor Concepts for Spacecraft Propulsion and Power (MSFC

Center

Part I, Project R.J. Litchford Marshall C.W.

University

National Space

Discretionary

Fund

No. 99-24)

and G.A. Robertson

Space

Hawk,

Director's

Flight

M.W.

Center,

Turner,

of Alabama

Aeronautics

Marshall

Space

Flight

and S. Koelfgen

in Huntsville,

Huntsville,

Alabama

and

Administration

Marshall

Space

January

2001

Flight

Center,

Center

,, MSFC,

Alabama

35812

Alabama

Final

Report;

Acknowledgments

The authors acknowledge the support of George C. Marshall Space Flight Center (MSFC), National Aeronautics and Space Administration (NASA), and the NASA Institute for Advanced Concepts (NIAC). This Technical Publication represents the Final Report (Part I) for MSFC Center Director's Discretionary Fund (CDDF) Project No. 9%24. The NASA Principal Investigator was Ron J. Litchford, TD 15/ASTE This technical

publication

has been reviewed

and is approved.

Garry M. Lyles Manager TD 15/ASTP Marshall

Available

NASA Center for AeroSpace 7i _i Standard-Drive Hanover,

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Space Flight Center

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(301) 621-0390

ii

TABLE

1.

INTRODUCTION

2.

FIELD 2.1 2.2

3.

3.2 4.

5.

7.

CONCEPTS

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

DIFFUSION

Armature Stator

Concepts

Concepts

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

,

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

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

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

COMPRESSION Field

ISSUES

DYNAMICS

Amplification

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

Flux

4.3 4.4

Skin Layer Methodology ............................................................................................. Armature Rebound Condition ......................................................................................

MARK

Skin Depth

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

4.2

5.1 6.

REACTOR

Propulsion Reactor ....................................................................................................... Power Reactor ..............................................................................................................

FLUX 4.1

1

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

COMPRESSION

MAGNETIC 3.!

OF CONTENTS

I DEVICE

Representative

MAGNETIC Analytical

6.2

Laboratory

CONCLUSIONS

Geometry

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

................................................................................................................ Calculations

DIFFUSION

6.1

REFERENCES

in Planar

Model

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

LABORATORY

EXPERIMENTS

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

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

Experiments

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

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

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

iii

3 4 9 14 14 16 19 19 21 22 26 28 29 33 33 37 38 39

_

z

LIST

°

Magnetic

flux compression

propulsion

°

.

and power

Average

reactor

thrust

of D-He

versus

of 65 percent

Schematic

of radial-mode

power

of SMES

,

Schematic

of flux compression

during

circuit

of magnetic

Illustration

Illustration

13.

200-MJ

circuit

4

fusion

power

8

electrical

processes

reactor

circuit

in the stator

power

reactor

armatures:

(a) metal-lined

11

12

14

in the Meissner state of the critical fields

field diffusion

concept

10

cartridge

as applied

17

and penetration

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

of flux skin depth

9

and armature

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

magnetic

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

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

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

stator

7

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

to a flux compression

reactor

driven

plasma

of transient an HTSC

Illustration

18

to flux compression

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

21

Measured electrical conductivity in a conical charge plasma jet of unseeded C4 ...................................................................................................................

28

Mark I configuration demonstration device

29

reactor 12.

flux compression

Illustration of superconductor field penetration and the Mixed state. Characteristic variation

through 11.

assuming

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

of explosively

for a type II HTSC 10.

fraction

extraction

coupled

diffusion

field compression

and (b) detonation

°

space

rate of 100 Hz with a nozzle

magnetic

coupled

Schematic

.

for integrated

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

,

Illustration

burnup

at a pulse

efficiency

with inductively

7.

concept

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

Computed effective expansion velocity and lsp for a D-He fusion detonation ................................................................................................................

detonations

°

reactor

OF FIGURES

geometry

for a radial-mode explosively driven .........................................................................................................

V

LIST

14.

Illustration formation Computed

flux coefficient

16.

Computed

armature

i7.

Illustration

18.

t9.

Magnetic

rebound

of experimental diffusion

Characteristic through

(Continued)

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

15.

magnetic

OF FIGURES

magnetic

conducting penetration

for Mark

I ................................................................................

31

radius

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

32

configuration

through

a hollow

diffusion

hollow

29

time constant

cylinders

time delay

for examining

conducting

of various

characteristics

vi

pulsed

cylinder

for magnetic materials for BSCCO

33

................................................ field penetration

with g=1.8771 and aluminum

........................ tubes

...........

36 37

LIST

°

Nuclear

fusion

2.

Energy

3.

Metal

4.

Electrical

5.

High-explosive

6.

Tabulation

reactions

yield for major versus

plasma

of major fusion

armature

and magnetic

of geometric

practical

interest

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

fuels ...................................................................................... characteristics

diffusivity

characteristics

OF TABLES

properties

15

of common

17

as a function

vii

6

...................................................................... metals

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

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

form factor

6

of the tube radius

ratio ..........................

30 35

! i

!

:

=

i

-i _

i:i

LIST

BSCCO

Bi2Sr2CaCu20

C4

composition-4

D

deuterium

HEDM

high-energy

He

isotopes

HTSC

high-temperature

MHD

magnetohydrodynamics

P

products

R

reactants

SMES

superconducting

T

tritium

OF ACRONYMS

AND

x

density

matter

of helium superconductor

magnet

energy

storage

ix

SYMBOLS

NOMENCLATURE

a

inner

radius

of tube

b

outer

radius

of tube

B app

external

applied

magnetic

Be,1

first critical

Bc,2

second

Bind

induced

B surf

surface

C

speed

Ca

contour

of armature

Cs

contour

of stator

d

thickness

of the stator

D m

magnetic

diffusivity

E

electric

field

Eo

electric

field in _ature

Es

electric

field in stator

f

mathematical

fb

burn fraction

y,,

pulse

g

geometrical

go

gravitational

field

field level

critical

field level

magnetic

field

flux density of light surface

surface

J

function

rate form factor fiel_d_of_ Earth

X

NOMENCLATURE H

magnetic

(Continued)

intensity

initial magnetic

H_u,f

magnetic

i

instantaneous

io

initial current

specific

intensity

intensity

at stator

surface

current

impulse

J

current density

J_

armature

Js

stator

Jn

Bessel

L

inductance

Lo

characteristic

current density

current density function

time-varying

of the first kind of order

length of the reactor; generator

LL

fixed load inductance

mi

mass of ion i

mp

pellet mass

mR

mass of reactants

Ni

number of ion species

PL

power

r_(t)

time-dependent

q

initial radius

delivered

n

initial inductance

inductance

to load radius

of the plasma

armature

of the armature

xi

NOMENCLATURE

r_

internal radius

rt

turnaround

R

electrical

resistance

magnetic

Reynolds

e

m

of the magnetic

stator

number

flux skin depth

S¢,a

flux Skin depth in armature

S_,s

flux skin depth

t

time

T

average

u0

characteristic

ua

armature

uD

detonation

ui

velocity

of ion i

ui

average

ion velocity

Vo

flux containment

vL

load voltage

v,

flux containment

wD

specific

Wo

initial energy

Wa

energy

Wetec

flux containment

radius

s¢_

ZZS7:7

(Continued)

in stator

thrust plasma

velocity

velocity velocity

energy

volume

at the beginning

volume

at the turnaround

of armature

expansion

point

of detonation stored

dissipatedin

in the load the armature

:_

extracted

electrical

energy

xii I[

NOMENCLATURE

_et

propulsive

jet energy

%

kinetic

energy

wL

energy

delivered

Wm, o

original

Wm, t

magnetic

Ws

energy

dissipated

rn

Bessel

function

Z

height

of the reaction

a

fusion

mass fraction

an

roots of equation

(74)

zlm

total mass defect

for the fusion

field energy

field energy

distance

in the reaction

at the turnaround

in the stator of the second

rlj

magnet

nozzle

_k

global

2c

flux coefficient

energy

kind of order

the penetration

efficiency conversion

permeability

armature

expansion

density electrical

of detonable

n

reaction

efficiency

magnetic

point

circuit

parameter conversion

chamber

chamber

time defining

energy

Po

of the exhaust

to load

magnetic

characteristic

(Continued)

efficiency

ratio material

conductivity

xiii

time of the magnetic

field through

the stator

NOMENCLATURE

%

characteristic

electrical

characteristic

time for field diffusion

characteristic

time for field compression

characteristic the detonation

time defining plasma

magnetic diffused

conductivity through

the penetration

flux magnetic

(Continued)

flux

xiv

hollow

tube

time of the magnetic

field through

TECHNICAL

MAGNETIC

FLUX

FOR

PUBLICATION

COMPRESSION

SPACECRAFT

REACTOR

PROPULSION

CONCEPTS

AND

POWER

1. _TRODUCTION

Driven tious

mission

months

by the desire goals

rather

for fast, efficient

for future

space

flight.

interplanetary These

than years

and improving

propulsion

translated

into a specific

power

can be roughly

goals

transport,

include

capability

NASA

has set a number

accomplishing

by a factor

goal of 10 kW/kg

missions

of 10 within

for the onboard

impulse (Isp) goal of 10,000 sec in combination with a thrust-to-mass ratio 10 -3 g for the spacecraft propulsion system. The principal technical challenge pulsion

systems

exhibiting

Unfortunately, day technologies velocity

most highly

are either

acceleration of desired

but would

heavy

technical

lean microfusion flux within magnetic

promising

detonations

pressure,

Methods

inordinately

large

drivers

and a specific

(acceleration) in excess of is the development of pro-

are within

the capabilities

of present

such that the acceleration

the nuclear

thermal

thruster,

propellant-to-payload

products

nozzle,

extracting

This is an integral

for the subsequent

in target

and

in target

reactor

concepts design

technologies

plasma

time to final

could

mass

plasma

are then collimated

can yield

ratios

achieve

the

to reach

the

is extremely

principles.

that compresses

and expelled

from

compressed the energy

needed

an indirect

if

for practical

magnetic needed

The and

field

can

to power

the

mode

of operaelectric

these

confinement

nozzle. m/sec

is used to drive high-power

for spacecraft

For example, inertial

of 106-107

the

reactor

by increasing

by a magnetic

levels

neutron-

the magnetic

reversed

since

high. Furthermore,

power

merit reassessment including

cloud

that are beyond

In this scheme,

is ultimately

the Isp and acceleration

power

concepts

1-|4

can be on the order

of the scheme electric

competing

pulse thruster.

expansion

detonations

electrical

detonation

several

diamagnetic

component

_ detonation-driven

flux compression

among

thermonuclear The

in these

by a magnetic

in which

approach,

structure.

velocity

for inductively

tion is conceivable thrusters.

advances

which

very low impulse,

form an expanding

and the detonation

also be envisioned.

developments

systems

One exception,

is a low-yield

reactor

expansion

effectively collimated interplanetary flight.

Magnetic

or yield

alternative

capabilities,

a semienclosed

charged-particle

standoff

require

powerplant

criteria

and very high lsp attributes. propulsion

interest.

15 yr. These

within

final velocities.

A particularly our modern

recent

very

efficient

is too long to be of lasting

desired range

rapid acceleration

of ambi-

to Mars

applications, schemes fusion,

based on modern could

15 staged

capitalize microfusion

on

schemes,4,14,16,17 magnetized targetfusion,18,19 andfastignitionantimatter-initiated nucleardetonations. 2°-22It is alsoconceivablethatchemicaldetonationsutilizing advancedhigh-energydensitymatter(HEDM) chargescould attainlimited successif theresultingplasmacloudsdemonstratethe requisitediamagnetic properties. Moreover,inductivestoragepowerreactorsbasedon field compressionprocesseshavebeenproposedasa prime pulsepowersourcefor high currentstandoffdriversandasa direct conversiontopping cycle for pulsed fusion systems. 23-28In comparisonwith capacitorbanks, inductive energy storage devicesaregenerallymorecompactandlesscostly andavoidthe needfor initial openingswitchesin the pulse-formingline. The possibleutilization of high-temperaturesuperconductors as a flux compression reactorsurfaceappearsto offer attractiveadvantages aswell. Theobjectiveof thiswork is to assessthesystem-levelperformanceandengineeringchallengesof field compressionreactorsas applicableto interplanetaryspacecraft.In particular,specialattentionis devotedtodeviceswhichcompressthefield betweena detonationplasmaarmatureanda superconducting stator_

2. FIELD

Magnetic

flux compression

chemical/nuclear the kinetic energy More

_

energy

kinetic

specifically,

a fraction

is extracted

armature

is fully expended

the armature

motion

reaccelerated

armature

processes

without

and return

the stored

In reactors

of this type,

magnetic

of circulating

currents

enough

to resist

magnetic

leads to consideration stator

materials From

stored

the device,

energy

inefficiencies

between

that are induced

field

penetration

during

of highly

conductive

detonation

with nonideal

the field compression

and the station-

surfaces.

In fact, the that are high

This criterion

plasma)

The all of

losses.

conductivities

process.

(i.e., fusion

of the

Of course,

armature

electrical

field while energy

of the armature.

the field compression have

sources

energy

surface.

field can reverse

production.

the fast-moving

within

and stator

thrust

stator

magnetic

magnetic

into

into electrical

conductive If the kinetic

as kinetic

as follows:

is first transformed

increasing

power.

for direct

associated

flux is trapped

only if the armature

electrical

then the compressed

from the device

process

is then transformed a highly

in a rapidly

as useful

conversion charge

energy

flux against

electromagnetic

to conversion

flux can be trapped

current

destroying

ary stator because magnetic

is temporarily

energy

detonation

This kinetic

seed magnetic

stator

can then be expelled

are subjected

The initial

armature.

of the energy

CONCEPTS

on a multistep

--, kinetic.

an initial

from the induced

REACTOR

are based

conductive

compresses

a portion

these

reactors

---) electrical

of a moving

as the armature

COMPRESSION

and highly

naturally conductive

(i.e., superconductors). the viewpoint

of global

energy

conservation,

these

reactors

obey the relation:

(1)

wje, + %lec : wk - % - v¢, : okwk ,

Wje t is the propulsive jet energy of the exhaust, Welec is the useful extracted electrical energy, W k is the initial kinetic energy of the detonation charge, W a is the energy dissipated in the armature, W s is the where

energy

dissipated Ideally,

substantially aligned chamber

in the stator the energy

circuit,

conversion

by real plasma plays

efficiency

processes

ion flow due to the ambipolar design

and r/k is a global

a significant

can exceed Furthermore,

role in terms

of magnetic

For a pure electric for propulsive

. power

reactor,

performance.

one is interested

For a propulsive

conversion 80 percent,

such as flute instabilities, potential.

sion efficiency.

concern

energy

electron the magnetic

diffusion

efficiency. but this value

could

Joule

effects,

heating

field configuration

losses

and magnetic

be reduced and fieldand reactor

flux compres-

= in achieving

reactor,

the highest

one is interested

possible

Wetec with little

in achieving

the highest

possible Wje t while also extracting the minimum necessary electrical energy that is needed to ignite subsequent detonation. Two reactor design concepts suitable for spacecraft applications are discussed section 2.1.

the in

3

2.1 The typical are situated amount

propulsion

to form

of driver

reactor

a magnetic

energy,

Propulsion

concept

mirror.

these reactors

is based

In addition, almost

magnetic

reaction

technical

variation

on the Daedalus

superconductor

a slight

acts as the reaction

chamber

chamber

on a concave

because

always

tion. The Daedalus-class paper,

Reactor

most

include

wall is considered.

magnet require

coil for electrical

power

integrated

approach.

a bulk-processed,

This concept

coils a large

genera6,7 In this

high-temperature

is illustrated

in figure

1.

Superconductor CompressionWall

Magnetic Field t Excitation

_ _

/ /

Structural Shell

\

/

FieldCoils--_

\

/

\

/

%

/

N

which

schemes

this highly

in which

around

fusion

a generator

exemplifies theme

surface pulse

\

- _" " "-.

" -

\?__.

/"

ElectricalPower [X]_

\

'guc; nr_

\\

DetonationTarget

/

Coil Exhaust

Figure

1. Magnetic space

flux compression

propulsion

reactor

concept

for integrated

and power.

In this concept, the plasma armature expands against a rearward-diverging by a set of superconducting coils. The magnetic flux is trapped and compressed high-temperaturesuperconductor (HTSC) sion process is reversed and the increased the reaction chamber

chamber.

wall,

sion process

The compressed

yielding using

By introducing mimmum low-weight

seed field,

and reduce

in_egrate_dpropulsion

A nuclear

stator,

pulse system

it should

and power

based

wall (i.e., stator). At some point, the expanacting on the plasma forces it out the rear of

field also produces

coil located

the overall

interplanetary

chamber pressure

component.

pickup

an HTSC

that can yield acceptable missions.

magnetic

a forward-thrust

an inductive

reaction magnetic

Electrical

be possible driven

trip times while

on this scheme

power

chamber.

can provide

from

The hoped-for nuclear

sufficient

performance

on the reaction the flux compres-

chamber.

flux diffusion

by low-yield

carrying

pressure

is extracted

to reduce

of both high jet powerand high lsp. Along these lines, it is instructive mance limits that can be achieved for various fusion fuels.

4

a magnetic

at the exit of the reaction

size of the reaction reactor

magnetic field provided between the plasma and a

levels

to compute

result

fusion

payload

losses,

reduce

is a compact,

detonation

to perform

the

pulses

meaningful

in the required

regime

the theoretical

perfor-

2.1.1

Energetics Starting

disassembly, blowoff

with the assumption

the fusion

mass

which

same throughout

energy

that after the nuclear

is averaged

did not undergo

the fireball

by collisions

reaction.

After

and the following

fbAmc

m i is the mass

of ion i, u i is the velocity

are quenched

by the hydrodynamic

among

all the particles

in the plasma

complete

thermalization,

the energy

relationship

lmiu2 where

reactions

for energy

conservation

including

per ion is the

can be written:

2

(2)

,

Ni

the

of ion i,fb is the burn fraction,

Am is the total mass defect

for

the fusion reaction, c is the speed of light, and N i is the number of ion species generated per reaction. Neutrons are neglected because they carry no charge. Only the momentum of charge particles can be electromagnetically fraction

manipulated

that is converted

for direct

to energy

m R = _-_R mi" From

production.

by the reaction

lmiu2

where

thrust

-

By introducing

(o_ = AnmR),

fba

(3)

Ni

conservation

considerations,

the following

relationship

the summations

over all ion species. an expression

are over the reactants Equation

for the effective

(R) and the products

(3) can now be used to eliminate ion expansion

velocity

(P) and the overbar

u i on the fight-hand

as a function

the mean

ion mass is defined

an average

side of eq. (4), such that

c2

(5)

by

m--i--l[(l-fb)ZRmi+fbZpmi]

The theoretical

denotes

of the burn fraction:

J fb_nR

where

is obtained:

(4)

miui:_[(1-fb)ZRmiui+fbZpmit'i]

where

for the mass

to write eq. (2) in the form:

mR c2

2

momentum

it is possible

a parameter

I w may now be computed

•

by noting

I _ miuil____p-m___ mi =ui

(6)

that

,

(7)

5

or whenreferencedto the Earth'sgravitationalfield,

/sp= where

(D) and tritium denote

cross sections

charge

of practical

of helium

(i.e., number

of nucleons).

fusion

fusion

approximately which

reactions

reactions

cross

are useless

Table

Practical ignition

of charged

considerations energy

particles,

production

1 where

the subscripts

the atomic have

mass

number

similar

valued

yield

parameters

to note that the D-T and D-D reactions

and are easier

to ignite;

of the reaction

for space

such as deuterium

of the fuel. The energy

energy

propulsion

however, in the form

applications,

reactions

of major

practical

they

release

of neutrons

since they cannot

[W= 4.03 MeV]

2He3(0.82MeV) + on1(2.45 MeV)

[W= 3.27 MeV]

2He4(3.5MeV) + on1(14.1 MeV)

[W= 17.6 MeV]

2He4(3.6 MeV) + _pt(14,7 MeV)

[W= 18.3 MeV]

yield for major

fusion

fuels.

Reaction Products

D-D

1T3,lp 1

9.9 xl013

1.1 x 10-3

D-D

2He3, 0nl

8.1 xl013

9.0 x 10-4

D-T

2He4, 0nt

3.38x1014

3.75× 10-3

D-He

2He4, lp 1

3.52 xl0

3.91 x 10-3

compel

w(J/kg)

the use ofD-Heas higher

of the primary

indicate

TM

a fusion

for D-He,

can be electromagnetically

calculations

interest.

1T3(1.01 MeV) + lP1(3.02 MeV)

Fuel

due to D-D reactions

secondary T. However, D-He reactions. 6

fusion

2. Energy

is substantially

which

reaction

in table denote

of the D-D reaction

50 percent

respectively,

and wasteful

1D2+ 1T3 -_ 1D2+ ID2 1D2+ 2He3

Table

required

are given

branches

roughly

of hydrogen

means.

l. Nuclear

D-T I D-D I D-He

reactions

and the superscripts

and neutron

than the D-He

for flux compression

isotopes

in table 2. It is important

and 35 percent,

by electromagnetic

involve

(He). These

consumes

are given

sections

80 percent

be manipulated

6

(8)

interest

of protons)

The proton

such that each branch

for the various larger

fusion

(T) and isotopes

the nuclear

(i.e., total number

neutron

'

go = 9.81 m]s 2. The nuclear

have

go

fuel for space

the reaction

manipulated.

products Of course,

fuel and D-T reactions

that the number

of neutron

propulsion. will consist

Although

there will always between

reactions

the

predominately be some

the primary

D and

can be 1 can be

that

having

detonation

plasmas

a high electrical

for both low magnetic

prone t0_substantial

technical

improve

depending

using

in the open

conductivity,

diffusivity

energy

risk,

and high

of pure

metals

be able to

efficiency.

behavior

tend

state, the penetrating

should

conversion

on their characteristic

comprised

In the Meissner

a phase

the material

transformation

in a flux compression

and magnetic

are marginal

to repel

in the presa penetrating

field is completely

repelled

of the superconductor.

For type i superconductors, conductors

into two types,

effect.

a metal

and significantly

I superconductors

flux due to the Meissner

from the interior

to achieve

high and R m >> 1,

manner. Alternatively, possible utilization of a type II field as it is compressed outwardly by the expanding

although

losses

in order

Concepts

the demands

material strength in a relatively straightforward HTSC reaction chamber to confine the magnetic

velocities

on the product

this hope has yet to be demonstrated

is to utilize

In this way, one can satisfy

primarily

are extremely

values

It is believed

R m > 1, although

3.2

depends

and high expansion

the characteristic

plasma-jet

may achieve

number

both of these parameters

detonations,

designed

materials

conductivity

detonations,

chemical

Reynolds

field strength)

a type I superconductor devices.

is =0.2

perfectly

to the normal

application

defining

is either

state. The major

is the low threshold

critical

transition

T, which

is far too

conducting values

to the normal

and exists

obstacle

in the Meissner

in using

type I super-

(i.e., temperature,

current

density,

state. The maximum

critical

field for

low for practical

application

in flux

compression

=

Ceramic-based sion applications temperature

type II superconductors,

due to the high critical

is above

tivity can persist

liquid

nitrogen

_underapplied

defines

the limiting

applied

field exceeds

tized amounts

value

threshold fields

however,

for maintaining

Be, l, the material

of flux. These

points

values

temperatures

magnetic

In a type II superconductor,

on the other hand, which

enters

of current

100 T.

==

there are two critical

field levels.

a true Meissner the so-called

of penetration,

known

useful

can be obtained.

over a wide range exceeding

are potentially

state mixed

state where

For example,

densities,

the critical

and superconduc:

The first critical

and is normally

as fluxoids,

for flux compres-

very small.

the field penetrates

may be envisioned

field (Be, l) When

the

in quan-

as circulating

vortices of current. The second critical field level (BCI2) defines the transition to the normal state, and it can be large enough for practical flux compression application. Flux penetration in both the Meissner state and the mixed state as well as the characteristic schematically

16

in figure

9.

variation

of the critical

fields fo r a type II HTSC are illustrated

B

Quantized Flux Vortex

Bc,2

Type II Superconductor

(Fluxoid) Normal State _

Bc_)CTanlExceed

Bc, 1

Bc,1 < B < Be,2 Mixed State

B< Bc,1 Meissner State

Figure

of the fluxoids

that is, a fluxoid

encompassing

superconductor

inhibited.

broken

and gives loose

function

from

tance

pinning

voltage

and

fluxoids

effective

can be non-negligible

a particularly exacerbating under these circumstances,

resulting

resistance rapidly,

Since

properties;

causes

through

a field gradient force

is small,

of the flux through

the

in the super-

fluxoids

can be

the conductor

as a

in a type II superconductor. field is not intense,

will be essentially giving

its conductive

and its free motion

the pinning

in a net creep

voltage

alters

altered

as flux pinning,

in the material.

centers,

is low and the magnetic

will migrate

has its energy

known

in an effective

density

in the superconductor

to a defect

This phenomenon,

rise to a net current their

If the current densities,

with defects

or adjacent

of time. This results

induced

" T

9. Illustration of superconductor field penetration in the Meissner state and the mixed state. Characteristic variation of the critical fields for a type II HTSC.

The interaction

conductor

Tc

zero.

At very

rise to a phenomenon

in the flux flow case, and breakdown

flux creep high

called

is insignificant fields

and

and the

high

current

flux flow. The effective

to the normal

state can ensue.

issue when the flux skin depth is small and the induced the current density can be very high and may exceed

resis-

This can be

current is high; because the critical value for the

HTSC. Note below

that the magnetic

that of the best metals,

netic diffusivity

characteristics

that the diffusivity values for various

diffusivity even

of a type II superconductor

in flux flow mode.

of various

For instance,

superconductor

can range from 10 -2 to 10 -6 m2/sec. metals as indicated in table 4.

Table

4. Electrical

Parameter

and magnetic

Dimension

Po (20 °C)

p_ • cm

Go (20 °C)

106(.Q • m)-1

Om=(_oOo)-I

m21sec

can be several

diffusivity

recent

materials

under

29'30 This

range

properties

studies pulsed

Aluminum

1.7

6.2

2.8

63.3

15.7

39.2

5.10

magnetic

of common

Brass

2.04

of magnitude

investigating

can be compared

Copper

1.26

orders

fields

the magindicate

with nominal

metals.

Stainless Steel 72 138 58

17

It is clear field. Therefore,

that for a type II HTSC, some of the major

HTSC materials to magnetic characteristics in the mixed pulse

fields,

will occur

that need to be answered

is that the transient

The anticipated

an intense

magnetic

field will exhibit

a penetration

magnetic

field

profiles

in the stator

time longer

magnetic are

plasma

For practical

(TO).

purposes,

than the charac-

is illustrated schematically in figure 10 magnetic field H inside a radial-mode

wall are shown

at various

during the armature expansion process. Note that there is some characteristic etration time of the magnetic field through the stator and some characteristic time of the detonation

pulsed

(1) How resistant

down?

teristic pulse time of the armature expansion process. This concept where a section of the HTSC stator wall is shown with an increasing reactor.

under

are as follows:

field penetration in the mixed state? (2) How good are the magnetic diffusion state? and (3) How does the HTSC material behave under intense applied-

and will it break

The hope

flux penetration

questions

it is necessary

instances

in time

time (At e ) defining the pentime defining the expansion that At[, > r D.

Superconductor

H

A

COHPression Wall--_H3 e._,,_,_1 d Field

H2

H1

Field Penetration T_e

Ho' I

t

_tp _

Figure

10.

Illustration

r

of transient

magnetic

and penetrati0n='t_ough

The HTSC cant research be categorized

stator

concept

is entirely

issues that must be addressed as follows:

(1) Breakdown

hypothetical

stator.

at this point and there are a whole

prior to practical

implementation.

of HTSC

strong

under

magnetization, (3) Joule/neutron heating of the material, (5) bulk processed versus wire fabrication.

t8

field diffusion

an HTSC

pulsed

(4) structural

The major fields,

integrity

host of signifi-

uncertainties

(2) hysteresis under

cyclic

cycling loading,

may of and

4. FLUX

Accurate instructive approach

analysis

to develop is adopted

This analysis ture rebound

of the reactor

a simplified here,

includes criteria.

COMPRESSION

analytical

and a simple

finite

requires model

model

conductivity

The modeling

radial-mode

and attempts

is described

of the MHD the dynamics reactor

to quantify

in sections

equations;

of flux compression.

developed

(illustrated

flux diffusion

4.1 through

however,

it is This

in fig. 4).

losses

and arma-

4.4.

Field Amplification

expansion of the plasma armature, some fraction of the trapped magnetic flux and the stator. The flux which escapes from the annular containment region

is lost for further

compression

cation,

losses,

including

solution

for describing

forthe

effects

approach 4.1

During the explosive will diffuse into the armature

formal

DYNAMICS

and represents

may be expressed

an inefficiency in terms

in generator

performance.

of the flux coefficient

as defined

The field amplifiin eq. (12):

-ra or

(22)

where

rs is the internal

armature,

radius

of the magnetic

and ra(t) is the time-dependent Differentiation

flux containment

radius

of the plasma

stator,

r i 1

Jet

measurement

12 shows

composition-4

representative Reynolds

device,

je_a_d

thai a Cohesive,

Figure

of unseeded

Inserting

for the magnetic

for a practical

observed

of 3x 104 m/sec.

jet from a 44 _ Cavity charge

the measured

of the plasma

been

applications

in a conical

charge

A practicaldemonstrationdevicecanbe developedusing a non-nuclearplasmasource,basedon theseresults.A demonstrationdevicealongthe lines of the Mark I configurationdepictedin figure 13 would be a logical stepin this direction.This deviceis envisionedasa l/2-m-diameterreactionchamber, which usescolliding plasmajets from opposinghigh-explosivechargesto producea radially expanding armature.The formationof a radially expandingplasmajet from two colliding jets hasbeenpreviously demonstratedon a smallscale.32The observedcollisional processin theseexperimentsis illustratedin figure 14.

Shielding

Magnet

Shell _

Coil

PrecursorIonization Generator

Plasma

Coil

Armature

I

)H m

t t| I

_

Shaped Charge x-- RadiallyExpanding

Explosive

PlasmaArmature

Figure

13.

Mark

I configuration

mode explosively stration device.

for a radialdriven

As a precursor been

analysis

performed.

to the Mark Typical

Illustration

of plasma

jet

collisional process and radial armature formation.

Representative

The calculations

stator materials were investigated. tions are summarized in table 5.

14.

demon-

5.1

ogy have

Figure

Calculations

I configuration, presume parameters

calculations

an internal

generator

for high-explosive

based

on the skin layer methodol-

diameter detonations

of 0.5 m and various used in the calcula-

29

Table

The variation 15. Numerical ing stator

materials

of steel,

copper,

diffusivity

increasing

compression

for HTSC

is not as encouraging

significant

increase

value

Calculations figure

efficiency

5 × 108 J/kg

Velocity(uo)

1 × 104 m/sec

on the magnitude

was observed as desired.

for magnetic

efficiency

Reynolds

numbers.

Reynolds

losses,

stator

of initial

stator

material,

of unity,

although

an

the result

is increased

to 10, a

seed field were The ..........results

carried

out

are presented

in

initial seed field, the value of which

impact.

system

10, assum-

number

increases,

in figure

materials.

is a minimum

to avoid

HTSC

number

of 50 percent.

the seed field and minimize

of 1 and

Reynolds

Reynolds

as a function

There

numbers

conductivity

for all stator

efficiency

ratio is shown

For the hypothetical

the magnetic

radius

expansion

With a magnetic

was noted

turnaround

of flux diffusion

HTSC.

as the material

When

conversion

to reduce

of the armature

was assumed.

an energy

magnetic

high R m, it is possible

as a function

and a hypothetical

for the armature assuming

16 for various

depends

SpecificEnergy(wo)

of 10 -5 m2/sec

in compression

stator

1,700 kg/m3

of eq. (60) was performed

a magnetic

characteristics.

Density(Po)

in the flux coefficient

integration

for a copper

5. High-explosive

With

a good

stator

material

and

size and weight.

Apparently, significant flux compression can be accomplished at marginal magnetic Reynolds numbers when the stator material is sufficiently resistant to magnetic diffusion. Thus, it appears that a successful demonstration The

preceding

pessimistic simplified

3O

device analysis

predictions analysis

could be developed,

which utilizes

is highly

of course,

idealized,

with respect

results

appear

to the minimum

encouraging.

a non-nuclear

high-explosive

and real hydrodynamic required

magnetic

effects

Reynolds

...... plasma will

number;

jet source.

lead

to more

however,

the

1 0.9

-,,-\ 0.8 0.7 0.6

_ _

\\_

ML_ ,m

,u

¢D O

•

0.5

\\'\ Stator Material

Rm=l

\

_= 0.4 UL -

-

Supecronductor

0.3 -

"

Copper Steel

_ \\_x_, \

'\ \ "_,

0.2 0.1 0 0

I

I

I

0.25

0.5

0.75

\_

ralrs

Rm= 10

\ %

\ \ \ \

\ \

¢D m ¢J m

\

Stator Material

==

\

o C._

Superconductor Copper Steel

= _L

\ \ \ \ \ \ \

\ \ I

1

0.25

0.5

0.75

fairs

Figure

15.

Computed

flux coefficient

for Mark

I.

31

1

-

0.9 _ 0.8 0.7

\

' \

I

High-Explosive Charge

iI

CopperStator

' ' \

\

0.6 ---

0,5

_

'%,

._

0.4 0.3

5 10 I00

0.2

"_'_-_

0.1

0

I

I

I

i

1

2

3

4

Bo (T)

Figure 16.

Computed

armature rebound radius.

i =

=

=

= = lit m

Ii

Z

z

J

m

32 Z

6.

MAGNETIC

DIFFUSION

LABORATORY

6.1 Analytical As part of this research, diffusivity

characteristics

configuration

in these

by a solenoid,

which

time-varying

magnetic

with respect treatment

experiments,

laboratory

samples

field inside

to the magnetic experimental

diffusivity diffusion

results

17, is a hollow magnetic

the solenoid

properties

process

designed

magnetic

is pulsed,

yields

In sections

a conducting

the magnetic

fields.

tube of test material

field on demand.

of the material.

through

to investigate

to strong-pulsed

external

once

were

exposed

in figure

a pulsed

the tube,

Model

experiments

when

as illustrated

can be used to create

of the magnetic

preliminary

simple

of HTSC

EXPERIMENTS

hollow

The basic surrounded

Measurement

quantitative

of the

information

6.1 and 6.2, an analytical

cylinder

is described

and the

discussed.

I I

_Hz(t) ,

No

! !

,

/o

d Figure

17.

Illustration

of experimental

for examining through

The magnetic equation

derived

diffusion

equation

diffusion

through

from Maxwell's

pulsed

a hollow

a conducting

electromagnetic

configuration

magnetic

conducting

hollow

diffusion cylinder.

cylinder

laws. In a cylindrical

is governed coordinate

by a magnetic system,

diffusion

the governing

has the form 33

02H Or 2

I___H r Dr

1 OH_ Dm

(69)

Ot

33

and the following

initial/boundary

conditions

apply: 33

Hz(b,t)=

(70)

H0

(71)

Hz(r,O):O

dt The solution transform given

to this system

methodology.

for/1R

a

a

of equations

1

L t)r Jr=a is known

The field Hz(t) = Hz(a,t),

which

mathematical

physics

using

the Laplace

of the conductor,

can be

= 1 in the form 33

oo

Hz(a,t)=

Ho-4Ho

2

J2(aan)JO(ban)

e -Dma2t,

[

(73)

(aa,,)_02 _-_ani---J-_a_,,)11 '

n=l

where

from

is built up in the cavity

the a n are roots of Jo(ba)Y2(aa)

and Jn and Yn are Bessel After

functions

a long enough

- Yo(ba)J2(act)

of the first and second

(74),

= 0

kind of order

n, respectively.

time, such that

1

(75)

t>w,

it is sufficient

to retain

only the first (n = 1) term. The field growth

-t/_

1

)

in the conductor

is then

(76)

where 1 r 1-Dma?-41rD

34

b2

(77) mg•

The parameter

g, defined

by

47_

g(bal

is a geometrical

form

factor

which

Table

In our = 7.14375 be estimated material

according

for the HTSC will depend

experimental

diameter

of b = 1.508125

efforts

tabulated

as a function

a/b

g

a_

0

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60

2.173 2.173 2.172 2.170 2.164 2.153 2.133 2.102 2.059 2.00t 1.926 1.833 1.720

0.65 0.70 0.75 0.80 0.85 0.90 0.95 0.96 0.97 0.98 0.99 1.00

1.587 1.431 1.253 1.052 0.8267 0.5766 0.3011 0.2430 0.1838 0.1236 0.0623 -

the tube

= 30.1626

size was

cm. Thus, g = 1.8771 are summarized

on the behavior of previous

(from

in figure

length

= 75 mm,

an inner radius times,

18. Actual

D m is anticipated

under

assuming

diffusion strong

wall

of a = 0.079375

table 6) and the characteristic diffusion

of the superconductor

researchers,

as follows:

mm. This yields

to eq. (77). The characteristic material,

of the ratio a/b in table 6. 34

6. Tabulation of geometric form factor as a function of the tube radius ratio.

experiments,

mm, and outside

outer radius values

small-scale

has been

(78)

-2 ' )

diffusion

a range

characteristics pulsed

to fail in the range

fields.

thickness cm and an time may

of conductivity of the HTSC Based

on the

of 10 -5 to 10 -3 m2/sec.

35

Superconductor Tube

1°2 F 101

di= 1.6 cm

(3,seL)

10° I 10-1

_

d0=3 cm

----......

I

Anticipated

/

Range _

Flux Creep

_

..... _

Kange TOrlyplcal Type II Superconductor

_

Iz 0 0

E

10-2 _

,i

I Flu×

0

10-3 _ 10-4

low

i

Copper E

Brass ................

10-5

. -........ r-, .........

. ........

Stainless Steel

10-6 )I

iili

10-7

loll

iII

III

I

I

10-7

104

Oil

llIIlI

i

I

I

10-5

10-4

IIi

oil

Ill

I

IIlll

.....

I

10-3

I

10-2

10-1

Magnetic Diffusivity(m2/secl

Figure

18.

Characteristic

magnetic

field penetration various

materials

through

diffusion conducting

time constant hollow

for magnetic

cylinders

of

with g = 1.8771.

i

m

m

| |

36 m

6.2 The objective (BSCCO)

of the experiments

superconducting

material

The experimental probe is placed

along

coil is looped

around

is submerged

in liquid

tested

in order

to compare

During and internal

testing,

materials.

for testing.

their magnetic

it can be expected

field shielded

sion characteristics

consists

of a cylindrical

diffusion

tube surrounded

by an excitation magnetic

the induced

materials

rate of Bi2Sr2CaCu20

x

metals.

the instantaneous

of measuring

Different

diffusion

current.

(i.e., copper,

coil. A Hall

field, and a Rogowski The entire

aluminum,

and

test section steel)

were

rates to that of the superconductor.

that a time delay

by the tube. From

of the material

the magnetic

with conventional

of the tube to measure

the tube and coil as a means nitrogen

Experiments

was to measure

in comparison

apparatus

the centerline

Laboratory

will occur

this experimentally

between

measured

the external

excitation

time delay, the magnetic

field diffu-

can be deduced.

Some typical results from these experiments are provided in figure 19 for aluminum and BSCCO These results indicate a time delay of =45 msec for BSCCO which may be compared with a time

delay

of 4 msec

ment

in penetration

for aluminum. delay

Although

preliminary

time and are sufficiently

in nature, encouraging

these

data indicate

to warrant

further

a significant

improve-

investigation.

MagneticFieldVersusTimefor BSCCOSuperconductor andAluminum Tubes 1,000 900 800 _"

700

Magn_

600 "

500

_ E

4oo

Applied _/M_t_CFT_n

,

o

, sclosu o,r e

300 200 100 0 20

40

60

80

100

120

140

160

180

200

Time,t (msec)

Figure

19.

Magnetic penetration time delay characteristics for BSCCO and aluminum tubes.

37

7. CONCLUSIONS

Magnetic based

flux compression

on our preliminary

can utilize

a detonation

way, one could the direct

A Mark Analyses achieve

assessment. plasma

develop

production

of the conductivity

power

fired

reactor

for spacecraft density

with a highly using

propulsion

systems

conductive

microfusion

can be designed stationary

or advanced

based on the assumed

has a significantly needed

lower

and velocity

reactor

driven

produced

sources.

bychem!cal

by shaped

A skin layer

the actual

plasma

armature

appear

surface

instabilities.

38

Conductivity

magnetic

to clarify

which

stator, in this

HEDM

analysis

charge

high explosive

targets

for

plasma

of the concept

jets

is also: proposed.

indicate

indicates

value,

diffusivity

small'scale

in comparison

system-level

benefits.

to be achieving

good

The major diamagnetic

laboratory

experiments

to conventional technical properties

meials,

that one

that effective

compression can be achieve d in a relatively moderate scale device. In addition, the potential field compression using type II HTSC stator materials Was evaluated, but the performance marginal

and power,

and thrust.

radial-mode

non-nuclear

feasible

that high-power

in c?nJun_stion

an intermittently

I demonstration

are technically

It appears

armature

of electrical

R m > 1 using

reactors

can flux

for improved gains were

did show that BSCCO but further

issues

associated

and

controlling

research

is

with the use of a Rayleigh-Taylor

REFERENCES

Winterberg,

.

Electron Hyde,

o

.

F.: "Rocket Beams,"

Fusion

Microexplosions,"

Hyde,

R.;

Wood,

L.;

Report

Society,

Journal

Martin,

A.R.;

°

Bond,

(ed.),

Martin

Winterberg,

Journal

Reupke,

Hyde,

Borowski,

12.

Orth,

Nuclear

Commission,

Fusion Fusion,

pp. 159-164,

Microexplosions,"

A Historical

Journal

The

Interplanetary

Review

G.R.

1974.

of the British

Propulsion

Society,

Daedalus--Final Society,

Vol. 32, pp. 403-409, Fusion

Systems

Part

I: Theoretical

on the the BIS Starship

Study,

pp. $44-$61,1978. System; Report

Part II: Engineering

on the BIS Starship

pp. $63-$82,

Microexplosions

Propulsion

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41

REPORT

DOCUMENTATION

PAGE

FormApp_ow,l OMB No, 0704-0188

Pubtic repoding burden for this collection of information is estimated to average t hour per response, Includ{ngthe time for revlewthg instructions,searching existing data sources, gathering and maintaining the data needed, and completingand reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operation and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington,VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503 1. AGENCY

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2. REPORT

DATE

January 4. TITLE

AND

3. REPORT

2001

TYPE

AND DATES

Technical

SUBTITLE

COVERED

Publication

5. FUNDING

Magnetic Flux Compression Propulsion and Power

Reactor

Concepts

NUMBERS

for Spacecraft

(MSFC Center Director's Discretionary Fund Final Report; Part I, Project No. 99-24) 6. AUTHORS

R.J. Litchford,

G.A. Robertson,

C.W. Hawk,*

M.W. Turner,* and S. Koelfgen* 7. PERFORMING

ORGANIZATION

NAMES(S)

AND

8. PERFORMING

ADDRESS(ES)

REPORT George

C.

Marshall

Marshal] Space

Space Flight

9. SPONSORING/MONITORING

Flight

Center,

Center AL

AGENCY

ORGANIZATION

NUMBER

M-995

35812

NAME(S)

10. SPONSORING/MONITORING AGENCY REPORT NUMBER

AND ADDRESS(ES)

National Aeronautics and Space Administration Washington, DC 20546-0001

NAS A/TP--2001-210793

11. SUPPLEMENTARY NOTES Prepared

for Advanced

*University 12a.

Space

of Alabama

Transportation

in Huntsville,

DISTRIBUTION/AVAILABILITY

Program,

Huntsville,

Space

Transportation

Directorate

AL

STATEMENT

12b.

DISTRIBUTION

CODE

Unclassified-Unlimited Subject Category 20 Standard Distribution 13.

ABSTRACT

(Maximum

200 words)

This technical publication (TP) examines performance and design issues associated with magnetic flux compression reactor concepts for nuclear/chemical pulse propulsion and power. Assuming that low-yield microfusion detonations or chemical detonations using high-energy density matter can eventually be realized in practice, various magnetic flux compression concepts are conceivable. In particular, reactors in which a magnetic field would be compressed between an expanding detonation-driven plasma cloud and a stationary structure formed from a high-temperature superconductor are envisioned. Primary interest is accomplishing two important functions: (1) Collimation and reflection of a hot diamagnetic plasma for direct thrust production, and (2) electric power generation for fusion standoff drivers and/or dense plasma formation. In this TP, performance potential is examined, major technical uncertainties related to this concept accessed, and a simple performance model for a radial-mode reactor developed. Flux trapping effectiveness is analyzed using a skin layer methodology, which accounts for magnetic diffusion losses into the plasma armature and the stationary stator. The results of laboratory-scale experiments on magnetic

diffusion in bulk-processed type II superconductors 14.

SUBJECT

TERMS

magnetic flux compression, electromagnetics 17.

are also presented.

SECURITY

CLAssIFIcATI()N

OF REPORT

Unclassified NSN 7540-01-280-5500

....

spacecraft,

propulsion,

power, superconductor,

15.

NUMBER

OF PAGES

16.

PRICE CODE

20.

LIMITATION

56 A04

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