CP620, Shock Compression of Condensed Matter - 2001
edited by M. D. Furnish, N. N. Thadhani, and Y. Horie
© 2002 American Institute of Physics 0-7354-0068-7/02/$ 19.00
THERMOPHYSICAL PROPERTIES OF HELIUM
UNDER MULTIPLE SHOCK COMPRESSION
Vladimir Ya.Ternovoi, Alexander S.Filimonov,
Alexei A.Pyalling, Viktor B.Mintsev, Vladimir E.Fortov
Institute for Chemical Physics Research RAS, Chernogolovka, 142432, Russia.
Abstract. The results on measurements of thermodynamic properties and electrical conductivity of
Helium compressed with shock wave reverberation technique up to pressure and density of 200 GPa and
1.4 g/cc are presented. The increase of the Helium conductivity up to the values of 1000 1/(Ohm-cm)
was found at the densities more than 0.7 g/cc and temperature more than 15 kK. Comparison of the
experimental results with different theoretical models of thermodynamic and transport properties of
shocked Helium was done.
INTRODUCTION
Being second after hydrogen in the set of
element abundance in universe, helium attracts
attention of theory due to simplicity of its atom
structure. Thermophysical properties of helium in
the Mbar pressure range at elevated temperatures
(0.5-5 eV) are of interest to astrophysical
researchers [1]. First and second ionization take
place in this region. However, up to now only one
dynamic experimental investigation have been
performed [2]. On the basis of these experiments the
semi-empirical EOS of helium [3] in the area of
high density and pressure was improved. Authors of
[2-3] did not consider ionization degree of shocked
matter because of high value of first and second
ionization energy (24.6 and 54.4 eV). Pressure of
helium metallization at low temperatures is
estimated about 11.2 TPa according to [3]. In a
liquid state and at elevated temperatures pressures
of the first and second ionization are considerably
lower than that in solid state, as well as, to result in
possible realization of these transformation in kinds
of plasma phase transitions (PPT) [ 4-7].
solid metal
2
3
4
Lg(T/K)
5
FIGURE 1. T-P phase diagram of helium from [4] with
traces of compression from ID hydrocode (connected
open squares). Predicted lines of constant mean charge are
marked by its value. Tr -triple point, C-critical point. Trs
-Ci,Tr 4 -C 2 -PPT
107
Three probe scheme was proposed for
resistance of the helium layer measurements with
Three
probe being
scheme
was charged
proposedprobes.
for It
shunt
resistance
between
resistance
of theto helium
measurements
withfrom
has allowed
removelayer
in-phase
handicaps
shunt
resistance
being
probes.
It
measuring
signal
andbetween
identify charged
the moment
of shock
has
allowed
to remove
in-phase
wave
reflection
from the
layer handicaps
boundariesfrom
at the
measuring
signal
and identify the
moment
of shock
final stages
of compression
(Fig.
2). Time
intervals
wave
reflection
from
the
layer
boundaries
at the
were measured at the initial stages of compression
final
of pyrometer
compression
(Fig. 2). Time intervals
withstages
optical
also.
were measured at the initial stages of compression
1D hydrodynamic simulation of the impact with
with optical pyrometer also.
EOS [3] was done. In Fig. 2,3 compression of
ID hydrodynamic simulation of the impact with
helium
initial Indensity
ρ compression
= 0.0582 g/cc
EOS
[3] with
was done.
Fig. 2,3
of is
analyzed
under
impact
of
steel
striker
of
thickness
helium with initial density p = 0.0582 g/cc is
1.5 mmunder
with impact
velocity
km/s on
sandwich of
analyzed
of 4.89
steel striker
of thickness
steel
bottom,
helium
layer,
sapphire
disk
(thickness
1.5 mm with velocity 4.89 km/s on sandwich
of
of
1,
5.28,
5.12
mm)
steel bottom, helium layer, sapphire disk (thickness
Thickness
of the used steel striker was small
of 1,5.28,
5.12 mm)
relative
to
the
initial
layer thickness
Thickness of the
usedhelium
steel striker
was small and
processto of
relative
the compression
initial helium was
layer accompanied
thickness and by
process
of from
compression
was surface.
accompanied
by to
unloading
bottom rear
This leads
unloading
from bottom
rearsteel
surface.
This leads
to
the diminishing
of the
– helium
boundary
the
diminishingand
of its
theoptical
steel - emission
helium boundary
temperature
during first
temperature
its optical emission during first
shock waveand
passage.
shock There
wave passage.
are two unloading waves in helium at
There
two unloadingFinal
waves
in helium
at
first
step are
of compression.
thickness
of helium
first
step
of
compression.
Final
thickness
of
helium
layer was chosen to be bigger than 0.1 mm to avoid
layer
chosen
bigger than
0.1 mm
avoid
the was
shorting
intoanbeelectrical
circuit.
It towas
10-30
the
shorting
in
an
electrical
circuit.
It
was
10-30
times smaller of the layer initial value. In the
times smaller of the layer initial value. In the
presented experiment hydrodynamic simulation
presented experiment hydrodynamic simulation
gave the decrease of T, P, ρ about 3, 7, 3 % during
gave the decrease of T, P, p about 3, 7, 3 % during
firstcompression
compressionof ofhelium,
helium,
release
first
duedue
to to
rarerare
release
wave.
At
latter
stages
unloading
wave
from
wave. At latter stages unloading wave from rare rare
surfaceterminates
terminates
process
of compression.
surface
thethe
process
of compression.
ThisThis
moment
was
indicated
in
emission
record
moment was indicated in emission record as aas a
momentofoftransition
transition
monotonically
decreasing
moment
to to
monotonically
decreasing
profile.
profile.
considerationof ofthe theprocess
process
InIn thethe consideration
of of
compressionmanually
manually
accepted,
compression
waswas
accepted,
thatthat
in Pin- ?U - U
coordinates
of of
reflected
waves
in steel
coordinatesHugoniots
Hugoniots
reflected
waves
in steel
coincide
with
itsits
isentrope
andand
forfor
sapphire
-with
its its
coincide
with
isentrope
sapphire
–with
first
Hugoniot.
Time
of
first
reverberation
in
steel
first Hugoniot. Time of first reverberation in steel
bottom
optical
record
waswas
used
for for
estimation
bottomfrom
from
optical
record
used
estimation
the
time
of
compression
termination.
The
bottom
the time of compression termination. The
bottom
thickness
was
taken
as as
thethe
thickness
of of
thickness
was
taken
thickness
Line of the assumed plasma phase transition of
the first ionization in ? -? diagram (Fig. 1) begins
of the
assumed
phase transition
of
from Line
triple
point
on plasma
the melting
line with
first
ionization
P-T finishes
diagram in
(Fig.
1) begins
? the
=200
GPa,
? =1 kKinand
critical
point
from? =660
tripleGPa,
point
with
? =35onkK the
[4]. melting line with
P=200
and submit
finishes in
pointof
In GPa,
this T=l
paperkK we
thecritical
results
with
P-660
GPa,
T=35
kK
[4].
simultaneous registration of optical emission and
In this
paper of
we a submit
resultsunder
of
electrical
resistance
layer ofthehelium
simultaneous registration of optical emission and
multiple shock compression to pressure 100 –
electrical resistance of a layer of helium under
200 GPa, which is close to pressure of assumed
multiple shock compression to pressure 100 plasma
phase transition.
200 GPa, which is close to pressure of assumed
plasma phase transition.
EXPERIMENTAL SETUP AND RESULTS
EXPERIMENTAL SETUP AND RESULTS
Experimental assembly was cooled by liquid
nitrogen.
Helium initial
temperature
wasbyaccepted
Experimental
assembly
was cooled
liquid
equal
78 KHelium
- close initial
to nitrogen
boilingwas
temperature.
nitrogen.
temperature
accepted
Itequal
was 78
controlled
K - closebyto chromel-cupel
nitrogen boilingthermocouple.
temperature.
It was initial
controlled
by chromel-cupel
Helium
pressures
and densities thermocouple.
were varied in
Helium
pressures
and0.03-0.12
densities were
in
the
rangeinitial
of 5-27
MPa and
g/cc. varied
Stainless
the
range
of
5-27
MPa
and
0.03-0.12
g/cc.
Stainless
steel plates of thickness 1.5 - 1 mm accelerated by
steel
plates oflaunching
thickness gun
1 . 5 to
- 1 velocity
mm accelerated
by
the
explosive
5 - 8 km/s
the
explosive
launching
gun
to
velocity
5
8
km/s
were used to generate megabar pressures. Layered
were used
to generate
megabar intermediate
pressures. Layered
systems
[8,9]
with PMMA
layer
systems
[8,9]
with
PMMA
intermediate
allowed to obtain final velocities in the range oflayer
6.5to obtain final velocities
the range
of 6.58 allowed
km/s. Experimental
techniqueinused
to measure
8 km/s. Experimental technique used to measure
optical
emission and electrical resistance is
optical emission and electrical resistance is
analogous to that in [10-12].
analogous to that in [10-12].
1800
2000
t,ns
tns
2200
1
2
800
14
3
12
400
t8
0
t1
t2
t3
t4
10
t9
t5 t6 t7
8
Tbr, kK
U, mV
4
-400
6
-800
4
1400
1600
1800
t,ns
FIGURE2.2.Experimental
Experimentalsnapshot
snapshot with
with depicted
depicted moments
momentsofof
FIGURE
shockwave
wavereflection.
reflection.
shock
signalsfrom
from UU+and
andULLprobe;
probe;33–- brightness
brightness temperature
temperature
1,21,2– -signals
+
frompyrometer
pyrometer channels;
channels; 44 –- T
TV from
sensitive
channel
(T(Tbr)
)
from
from
sensitive
channel
br
br
(its y axis is linear from 3 to 7 kK)
(its y axis is linear from 3 to 7 kK)
108
Pmax
PPmax
max
120
120
120
2
11
3
2
24
3
35
4
46
5
57
6
68
7
79
8
810
9
911
10
10
12
11
11
13
12
12
13
13
100
100
100
80
P, GP
Pa
P , G P, aG P a
striker with velocity 8 km/s. Thickness of striker and sandwich
striker are
with
velocity
km/s.5.13
Thickness
of
striker
and
sandwich
layers
1.02,
1.05,8881.145,
mm. of
striker
with
velocity
km/s.
Thickness
of striker
striker and
and sandwich
sandwich
with
velocity
km/s.
Thickness
layersUsually
are 1.02,
1.02, 1.05,
1.05,
1.145,
5.13 mm.
mm.
layers
are
1.02,
1.145,5.13mm.
layers
are
1.05,
5.13
code1.145,
results
were used to calculate
1
80
80
60
60
60
40
40
40
20
Usually
code
results with
werefinal
usedpressure
to calculate
calculate
Usually
results
were
used
to
density
in thecode
experiments
150 –
density
in
the
experiments
with
final
pressure
150
in the
with
final
pressure
150
-––
density
experiments
with
finalsmall
pressure
150 of
230 GPa.
It experiments
is connected
with
value
230
GPa.
It
is
connected
with
small
value
of
GPa. It step
is connected
with
small
value
of
230
connected
with for
small
valuewith
of
compression
time intervals
a layer
compression
step time
time
intervals
for
layer
with
compression
step
intervals
for
intervals
for aaa layer
layer
with
thickness
of about
2 mm.
Such snapshot
and with
code
thickness
of
aboutin22Fig.
mm.
Such snapshot
snapshot
and
code
thickness
about
mm.
mm.
Such
snapshot and
and code
code
results
areof
shown
4. Such
results
are
shown
in
Fig.
4.
results
are
shown
in
Fig.
4.
shown
in Fig. 4. became more than 0.5
As a rule,
conductivity
As aawhen
rule, the
conductivity
became
more
than
0.5
As
rule,
conductivity
became
0.5
conductivity
became
more
thang/cc.
0.5
1/Ω/cm
density was
moremore
than than
0.7
1/Ω/cm
when
the
density
was
more
than
0.7
g/cc.
l/Q/cm
when
the
density
was
more
than
0.7
g/cc.
1/Ω/cm
the density
was moreofthan
0.7 g/cc.
We werewhen
interesting
in reversibility
the transition
Westates
were interesting
interesting
in
reversibilityItof
of
the
transition
We
were
reversibility
the
interesting
in
reversibility
ofwas
the transition
transition
to
with high in
conductivity.
measured
to
states
with
high
conductivity.
It
was
measured
to
states
with
high
conductivity.
It
was
measured
high
density hysteresis
of conductivity. It was measured
density
hysteresis
of conductivity.
conductivity.
density
of
conductivity.
Forhysteresis
illustration
of
a given thesis in Fig. 5 the
For
illustration
of
given
thesis
in
Fig.
the
For
illustration
of
thesis
Fig.
For illustration
of aaaofgiven
given
thesis in
inchange
Fig. 555 the
the
experimental
records
resistance
and
experimental
records
of
resistance
change
and
experimental
records
of
resistance
change
and
experimental
records of profile
resistance(open
change
and
brightness temperature
circles)
brightness
temperature
profile (open
(open
circles)
brightness
brightness
temperature
profile
(open
circles)
together
withtemperature
results of 1D profile
hydrocode
modelcircles)
density
together
with
results
of
1D
hydrocode
model
density
together
with
results
of
ID
hydrocode
model
density
together
with
results
of
1D
hydrocode
model
density
profile for first and end layer points (open and
solid
profile for
for
first
and end
end
layer points
points
(open
and
solid
profile
and
layer
and
profile
for
first
and
end
layer
points
(open
and solid
solid
squares)
forfirst
a given
experiments
are (open
submitted.
squares) for
for aaa given
given experiments
experiments are
are
submitted.
squares)
squares)
for
given
experiments
are submitted.
submitted.30
20
20
0
0
0
0
0
0
1
2
3
4
5
6
1
2
2
3
U , km
3 /s
4
4
5
5
6
6
1
U , km /s
U , km /s
FIGURE 3. P – U diagram of helium compression up
diagram
of
helium
compression
up
FIGURE
U diagram
of2,3helium
compression
up
to
114 GPa.3.3.1 –PPPsapphire
Hugoniote;
steel isentropes;
4 - up
12
––- UU
of
helium
compression
FIGURE
to
114
GPa.
1
–
sapphire
Hugoniote;
steel
isentropes;
12
114
1
2,34
1
–
manual
path
of
compression;
13hydrocode
results.
to 114 GPa. 1 – sapphire Hugoniote; 2,3- steel isentropes; 4 - 122
manualpath
pathof
ofcompression;
compression;1313hydrocode results.
13-hydrocode
results.
––—manual
0
0 100
100
0 100
100
Texp
Texp
Texp
200
200
200
300
300
300
400
400
t,I,ns
400
IB
t, ns
Pmod
Pmod
Pmod
500
500
500
tentr
tentr
tentr
600
600
600
600
-1
-1
-1
U,U,VU,
VV
t1
t
t11
UUU
T -
-1
-1
-1
ρmod
ρmod
ρmod
t2
t2
t2
exp
Texp
Texp
900
1000
1100
1200
900
900
900
1000
1000
1000
1100
1100
1100
1200
1200
1200
ρ0 = 0.033 g/cc
ρ = 0.033 g/cc
ρ00 = 0.033 g/cc
1300
1400
1500
1600
t, ns
t, ns
t, ns
1400
1400
1400
1500
1500
1500
1600
1600
1600
1300
1300
1300
30
30
25
25
25
20
20
20
15
15
15
10
10
10
5
5
5
0
0
0
FIGURE 5. Hysteresis of conductivity dependence on density.
FIGURE
Hysteresis
dependence
Hysteresis
of
conductivity
dependence
on density.
density.
FIGURE
5.
Open
and 5.
solid
squaresof
– conductivity
density
profile
near steel on
and
sapphire;
Hysteresis
of
conductivity
dependence
on density.
FIGURE
5.
Open
and
solid
squares
profile
near
steel
Open
and
solid
squares -– density
density
profile
near
steel and
and sapphire;
sapphire;
tOpen
time
of
conductivity
increasing
and
decreasing.
1, t2 –and
solid
squares
–
density
profile
near
steel
and
sapphire;
tj,
t , t2
t -– time
time of
of conductivity
conductivity increasing
increasing and
and decreasing.
decreasing.
t11, t22 – time of conductivity increasing and decreasing.
DISCUSSION
DISCUSSION
DISCUSSION
DISCUSSION
The results of measurements
measurements of
of the
the electrical
electrical
The results
of measurements
electrical
conductivity
of
dependence
density
are
conductivity
of helium
helium
dependenceof
onthe
density
are
The results
of measurements
ofon
the
electrical
conductivity
of
helium
dependence on density
are
placed
in Fig.
6. helium
In
the
spectrum
Fig.of
the experiments
experiments
wide
spectrum
conductivity
dependenceaa wide
on
density
are
placed
in Fig.
6. In therealized:
experiments
a wideupspectrum
of
plasma
states
densities
toto 1.5
plasma
states
istherealized:
densities
1.5
placed
in Fig.
6. Inis
experiments
a wideup
spectrum
of
plasma
states
is
realized:
densities
up to 1.5
33
33
g/cm
<≤
of
plasma
states is ~(1-20)*10
realized: densities
up to 1.5
temperatures
~(1-20)*10
K at
at pressures
pressures
3, temperatures
3 K
g/cm3 , temperatures
~(1-20)*10
≤
3 K at pressures ,22
22
concentration
to
g/cm
, temperatures
~(1-20)*10
K at up
pressures
≤
150 GPa
and an electron
up
to —10
~⋅1022
3 GPa and an electron concentration up to ~⋅10 22
150
-3
cm"
At
parameters
the
plasma
cm-3.GPa
Atandmaximal
maximal
parameters
the up
plasma
150
an electron
concentration
to ~⋅10isis
cm-3 . At maximal
parameters
the nonideal
plasma in
is
degenerated
nneeJ?
and
cm
. At maximal
parameters
the nonideal
plasma in
is
degenerated
50
and strongly
strongly
λ33 ~~ 50
degenerated
n
eλ3 ~ 50 and strongly nonideal in
relation to theneCoulomb
FΓ ==nonideal
Ek/E
degenerated
and strongly
in
interaction
Ek/EF F -10
~ 10
λ ~ 50 interaction
relation
to the Coulomb
interaction
= E3 /EF ~The
10
and
interatomic
repulsion
Fa = Γ
relation
to the Coulomb
interaction
/EF ~ 10
Γ n=araEkk~l.
U,U,VU,
VV
P,P,GPa;
T/160,
KK K
P,
GPa;
T/160,
GPa;
T/160,
100
100
100
0
tentr.
ttentr.
entr.
Tmod
Tmod
Tmod
exp
U+
U+
U
+
0
0
0
0
0
UΣ
U
UΣΣ
Uexp
Uexp
U
1
1
1
1
1
Tmod
Tmod
Tmod
200
200
200
1
. . .
T, kK;
10
g/cc
ρ,10
kK;
, g/cc
T,T,kK;
10
ρ,ρg/cc
compact material, flying away from striker after
compactThe
material,
flying away
away
from
strikerwaves
after
from striker
after
material,
flying
from
after
the compact
impact.
counteraction
of rarefaction
the
impact.
The
counteraction
of
rarefaction
waves
the
The counteraction
of rarefaction
waves
wasimpact.
considered
without taking
into account
was considered
considered
without taking
taking into
into account
account
was
materials
strength. without
materials
strength.of the process of compression in
materials
P-U strength.
diagram
P-U
diagram
ofinthe
the
of compression
process
compression
in
process
of
Fig.P-U
2 isdiagram
shownof
Fig.
3. The
parameters in
of
Fig.
2
is
shown
in
3.
The
Fig.
parameters
of
Fig.
2 is shown
in Fig.1D3. code
The simulation
parameters are
of
compression
according
compression
according
1D
code- simulation
simulation
ID code
are
compression
according
1D
submitted
also.
In the first
two
three steps are
of
three
of
submitted also.
also.
Incan
thesee
first
two -- three
steps of
submitted
the
first
two
steps
compression
oneIn
closeness
of parameters
parameters
compression
one can
can
see closeness
closenessinof
ofexperimental
compression
one
see
parameters
from
both methods.
Small
decrease
from
both
methods.
Small
decrease
in
experimental
from
methods.
decrease
experimental
time both
of these
steps Small
leads to
higher inhelium
density
density
time of
of these
these
steps leads
leads to
to higher
higher discrepancy
helium density
time
steps
helium
relative
to code
results.
This
is
is
relative
to
code
results.
This
discrepancy
relative
discrepancy
is
conservedtoupcode
to theresults.
maximalThis
pressures.
Difference
pressures. Difference
Difference
conserved up
up to
to the
the maximal
maximal pressures.
Difference
conserved
-2
-2
-2
-3
-3
-3
ns
in final
final pressures
pressures isis only
onlyt,about
about
4% while
while in
in density
density
in
4%
in
final
pressures
is
only
about
4% while in density
about
20
%.
– about
20 %.
in
final pressures
is only about 4% while in density
– about
20 %.
FIGURE
4. Experimental
Experimental and
and code
code snapshot
snapshot of
of helium of
FIGURE
4.
– about
20
%.
FIGURE 4. Experimental and code snapshot of helium of
->U/^n+ Oft O/
initial
density 0.078
0.078
g/cc compression
compression
under impact
impact
of steel
initial
density
g/cc
Experimental
and code under
snapshot
of helium
of
FIGURE
initial
density 4.0.078
g/cc compression
under
impact
of steel
initial density 0.078 g/cc compression under impact of steel
109
and interatomic repulsion Γα = nara3~1. The
electrical conductivity of plasmas is about 3 orders
electrical conductivity of plasmas is about 3 orders
of
relatively narrow
narrow
of magnitude
magnitude increases
increases within
within relatively
interval
of
densities
(ρ~0.7-1.25
g/cc),
achieving
the
interval of densities
(p~0.7-1.25 g/cc), achieving the
3
values
of
10
3 ohm/cm typical to that of the heated
values of 10 ohm/cm typical to that of the heated
alkaline
alkaline metals.
metals.
10000
kK [12]
• -- T=20-25
T=20-25kK[12]
a -- T=15-25
T=15-25 kK
kK
illustration of the dependence of the parameters on
particle radii curves were calculated for r=1.3 a.u.
and T= 10000 K. It is seen that sharp increasing
and T=10000 K. It is seen that sharp increasing
appears at more higher densities. The simplest
appears at more higher densities. The simplest
Debye-Huckel approximation gives plasma phase
Debye-Hückel approximation gives plasma phase
transition at densities of -0.1 g/cc (Curve DHA).
transition at densities of ~0.1 g/cc (Curve DHA).
More
close to the experiment is Ebeling's model
More close to the experiment is Ebeling’s model
[4].
[4].
This work was supported in part by Russian Fund
was supported
by Russian Fund
for This
Basicwork
Researches
Grant inNpart
00-02-17550.
The
for
Basic
Researches
Grant
N
00-02-17550.
authors thank V. K. Gryasnov for calculation The
of
authorsparameters
thank V. and
K. Gryasnov
for calculation
plasma
N. A. Afanas'ev
for his ableof
plasma parameters
and N. A. Afanas’ev for his able
assistance
with the experiments.
assistance with the experiments.
REFERENCES
REFERENCES
1. V. N. Zharkov, V.
P. Trubicin, Fizika planetnih nedr.
DHA
1000
T=30 kK
BDH+HS
ra=1.3 a.u.
σ, Mo/cm
100
10
T=20 kK
Min.Met.
ra=1.8 a.u
1
Ebeling
T=10 kK
0,1
IDEAL
0,01
Spitzer
collapse
Debye
collapse
0,001
0,001
0,01
, g/cc
g/cc
ρP,
0,1
M. Nauka. 1980, 448 p [Russian].
V. N. W.
Zharkov,
V. P.N.Trubicin,
Fizika
planetnih
nedr.
2.1.Nellis
J., Holmes
C, Mitchell
A. C.,
et al., PRL,
M. Nauka.
1980,
448 p [Russian].
53,
1248-1251
(1984).
Holmes
N. C.,A.
Mitchell
A. C.,
al., PRL,
3.2. Nellis
YoungW.
D.J.,A.,
McMahan
K., Ross
M.,etPhysical
53, 1248-1251
(1984).
Review
B, 24, 5119-5127(1981).
Young D.
McMahan
A. K.,
Ross
M., ThermoPhysical
4.3. Ebeling,
W., A.,
Forster,
A., Fortov,
V.E.,
et al.,
24, 5119-5127
Review B,
physical
Properties
of Hot(1981).
Dense Plasmas, Leipzig:
4. Teubner,
Ebeling, W.,
Forster,
A., Fortov, V.E., et al., ThermoStuttgart,
1991.
5. Forster
A.,Properties
Ebeling W.,
in "Strongly
coupled Leipzig:
plasma
physical
of Hot
Dense Plasmas,
physics",
by H.1991.
M. Van Horn and S. Ichimaru,
Teubner, eds.
Stuttgart,
University
Rochester
(1993) p.coupled
347. plasma
5. Förster
A., ofEbeling
W.,Press
in “Strongly
6. Schlanges
Bonitz
A., in
physics”,M.,
eds.
by H.M.,
M.Tschttschjan
Van Horn and
S."Strongly
Ichimaru,
coupled
plasma
physics",Press
eds.(1993)
by H. p.M.347.
Van Horn
University
of Rochester
and S. Ichimaru,
University
of Rochester
(1993)
6. Schlanges
M., Bonitz
M., Tschttschjan
A.,Press
in “Strongly
p.coupled
77.
plasma physics”, eds. by H. M. Van Horn
7. Forster
Kahlbaum
T., Ebeling
W., High
Pressure
and S. A.,
Ichimaru,
University
of Rochester
Press
(1993)
Research
p. 77. N 7, 375(1991).
8.
G.,Kahlbaum
et al., Zhurnal
Prikl. Meh.
Tehn.Pressure
Fiziki,
7. Ivanov
FörsterA.A.,
T., Ebeling
W., IHigh
Jfc
2, p. 86-90,
[Russian].
Research
N 7, (1982)
375 (1991).
9.
G.,etand
P. "High
sys8. McQeen
Ivanov A.R.G.,
al., March
ZhurnalS.Prikl.
Meh.explosive
I Tehn. Fiziki,
tems
equation-of-state
studies." SWCM - 1987.
? 2, for
p. 86-90,
(1982) [Russian].
Ed. by S/R.C/G.,
Schmidt
N. C. S.
Holmes.
Elsevier
Science
9. McQeen
and March
P. ”High
explosive
sysPublishers
B. V. New York, 1988,
pp. 107-110.
tems for equation-of-state
studies.”
SWCM - 1987.
10. Ed.
WeirbyST.,
Nellis W.J.,
Phys.Science
Rev.
S/ C/Mitchell
Schmidt AC.,
N. C. Holmes.
Elsevier
Lett.,
76, 1860(1996).
Publishers
B. V. New York, 1988, pp. 107-110.
11.
V.E., Mitchell
TernovoiA.C.,
V. Ya.,
Kvitov
V., etRev.
al.
10. Fortov
Weir S.T.,
Nellis
W.J.,S. Phys.
JETP
Letters
69,
926-931
(1999).
Lett., 76, 1860 (1996).
12.
V. Ya.,
Filimonov
A.S., Kvitov
Fortov S.
V.E.,
11. Ternovoi
Fortov V.E.,
Ternovoi
V. Ya.,
V.,etetal.,al.
Physica
8:265,6-12(1999).
69, 926-931 (1999).
JETP Letters
13.
S. V.
V.,Ya.,
Fortov
V. E., et
al.,Fortov
"Investigation
of
12. Dudin
Ternovoi
Filimonov
A.S.,
V.E., et al.,
shock
compressed
plasma
parameters
by
interaction
Physica B: 265, 6-12 (1999).
magnetic
SCCM-1997,
edited by S. C.of
13. with
Dudin
S. V., fild"
Fortovin V.
E., et al., “Investigation
Schmidt
et
al.,
AIP
Conference
Proceedings
429,
shock compressed plasma parameters by interaction
New
York,
1998,
pp.
793-795.
with magnetic fild” in SCCM-1997, edited by S. C.
14. Fortov
and AIP
lakubov
I.T., Physics
of Nonideal
SchmidtV.E.,
et al.,
Conference
Proceedings
429,
Plasmas,
Energoatomizdat,
Moscow,
1994
pp. 123New York, 1998, pp. 793-795.
165[Russ.].
15. Ebeling W., Physica, 43 293 (1969).
neλ3=1
1
10
FIGURE 6.
6. Helium
Helium conductivity
conductivity versus
versus density
density diagram.
diagram.
FIGURE
Thermodynamical parameters of helium are
Thermodynamical parameters of helium are
calculated in frames of plasma chemical model [14],
calculated in frames of plasma chemical model [14],
which takes into account Coulomb interaction in
which takes into account Coulomb interaction in
frames of Debye approximation in Grand canonical
frames of Debye approximation in Grand canonical
ensemble and repulsion of heavy particles using
ensemble and repulsion of heavy particles using
hard spheres approximation. The radii r=1.8 a.u.
hard spheres approximation. The radii r=1.8 a.u.
was choisen from the coincidence of the calculated
was
choisenoffrom
coincidence
the calculated
Hugoniots
liquidthe
helium
with theofexperiment
[2].
Hugoniots of liquid helium with the experiment [2].
To estimate conductivity we use x-approximation
To
conductivity
we use for
τ-approximation
[4], estimate
which gives
Spitzer asymptote
fully ionized
[4],
which
gives
Spitzer
asymptote
for
ionized
/2
Boltzmann plasma - cr~7^3/2/A, (A fully
- Coulomb
Boltzmann
plasma
σ~T
/Λ,
(Λ
Coulomb
logarithm) and in the case of the Fermi statistics /2
logarithm)
in the
the partially
case of the
Fermiplasma
statistics
a~Tp3/2
/AFand
. For
ionized
this1/2 this
σ~T
/Λ
.
For
the
partially
ionized
plasma
F
F
theory gives Lorentz approximation: cr~ne/naT 1/2Qea.
theory
gives Lorentz transport
approximation:
σ~ne/naT Qea.
(Qea - electron-atom
cross-section).
(QeaThe
- electron-atom
transport
cross-section).
results of calculations for the different
The results
of kK,
calculations
for Tthe
different
isotherms
T = 10
T - 20 kK,
- 30
kK in
isotherms
T
=
10
kK,
T
=
20
kK,
T
=
30
kKlow
in
dependence on density are placed in Fig. 6. At
dependence
density areofplaced
in Fig.
6. At low
temperaturesondecreasing
electrical
conductivity
temperatures
decreasing
of electrical
with the increasing
of density
changed conductivity
by its steep
with
increasing
of density
changed
by itsreason
steep
climbthe
after
some critical
density.
The main
climb
some
critical
The
main reason
of thisafter
effect
is so
calleddensity.
pressure
ionization
that
of
thisplace
effect
is sodensities.
called pressure
takes
at high
With theionization
increasingthat
of
takes
place at high
densities.
With the less
increasing
of
the temperature
this
effect becomes
apparent
the
effect
less apparent
and temperature
disappears atthis
very
highbecomes
temperatures.
For the
and
disappears
at dependence
very high temperatures.
For the
illustration
of the
of the parameters
on
particle radii curves were calculated for r=1.3 a.u.
110