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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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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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
1979.
System;
Report
The Propulsion
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41
REPORT
DOCUMENTATION
PAGE
FormApp_ow,l OMB No, 0704-0188
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2. REPORT
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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.
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OF PAGES
16.
PRICE CODE
20.
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56 A04
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