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Radiation effects in gas filled microballoons
Volume 77A, number 6
PHYSICS LETFERS
23 June 1980
RADIATION EFFECTS IN GAS FILLED MICROBALLOONS N.A. TAHIR and E.W. LAING Department of Natural Philosophy, The University. Glasgow G12 8QQ, Scotland Received 1 February 1980
Using a modified form of the computer code MEDUSA we study the effect of radiative diffusion in laser compression simulations of neon filled, thin glass microballoons. Our calculations show that the radiative preheat of the target reduces 5 kg/rn3 to 1.8 x i04 kg/rn3. the final gas density by up to a factor 3 while the final shell density drops from i0
1. Introduction. In previous publications [1,21 we have discussed modifications to MEDUSA [3] a single velocity, two temperature 1-D Lagrangian computer code, by inclusion of a steady state radiation physics model. In this model the total continuum radiation arising from free-free and free.bound transitions diffuses 8-
into the medium in an assumed Planckian distribution
using the Rosseland mean opacity. Our calculations do not take account of line radiation effects. The Rosseland mean opacity for the total continuum radiation is evaluated in our calculations using a simple LIE hydrogenic approximation given by ref. [4]. Using 8
tr50ps
t~ 5Ops
log Te
log
logTr
__
Te
__
(a)
(b)
2-
2Logy
Log ~
_______________________________
0
20
40
R (j~ml
________________
60
0
20
I
40
I 60
R (,um)
Fig. 1. (a) Dependence of log ~, log Tr and log Te on target radius at t = 50 ps, radiation transport included. (b) Dependence of log p and log Te on target radius at t = 50 ps, radiation transport excluded.
430
Volume 77A, number 6
PHYSICS LETTERS
this modified version of the code we have carried out numerous computer runs to study the transport of continuum radiation in a neon filled thin glass microballoon. The object of these calculations is to investigate the preheat effect which arises from the penetration of the medium energy photons created at the critical density, into the uncompressed target core where they deposit their energy. We do not study the emission spectrum which would require a more sophisticated multigroup photon model. The laser pulse parameter used in these calculations are well within the capability of the Nd glass laser at the Central Laser Facility, Rutherford Laboratory. The target parameters are also chosen to match approximately targets used in a number of experiments performed at the Rutherford Laboratory Laser Division [5] -
2. Details of the problem. The target used in these calculations is a glass microballoon with inner radius R1 = 35 sum.. wall thickness L~R= 0.9 .tm and filled with neon at 18 atmospheres at room temperature i.e. at a 3. A Gaussian laser pulse with total density of 15 kg/m energy —~7OJ is used to compress this target. The peak power in the pulse ~m is —P700 GW and pulse duration, T, is lOOps. Experiments suggest that about 10% of 8
-
t:BOps
the laser energy is absorbed under these conditions and the remainder reflected. This partial absorption is treated in the code by inclusion of a factor in the absorption subroutine. No attempt is made to treat the reflection of the laser light. For comparison we have stimulated the compression of this target with and without radiative transport and the results are plotted in figs. 1—4. Figures labelled (a) correspond to inclusion of radiative transport while (b) denotes cases where radiation is excluded. In the latter case the energy is transported by a flux limited electron thermal conduction model, while in the former case both electron and radiation thermal conduction are considered. Flux limiting prevents the code from over-estimating the thermal flux in case of large temperature gradients. Also in the case of no radiative transport, radiation self absorption is considered in the overdense core region whereas in the underdense corona region the radiation is allowed to escape freely. The degree of ionization in the two cases is evaluated by a steady state density and temperature physics model which assumes thedependent plasma toatomic be in ionizational equiibrium due to a balance between collisional ionization + photoionization and three.body + radiative recombination [6]. 8
:: ::
23 June 1980
t:BOps
-
:—‘~
(~)
2~0’
(b)
______
logy 610
log
-
I
R(,um)
RçM.nl) Fig. 2. (a) As in fig. 1(a) but at r = 80 ps. (b) As in fig. 1(b) but at t
=
80 ps.
431
Volume 77A, number 6
8
6
PHYSICS LETTERS
-
8 t =125ps
-
Te log log Tr
23 June 1980
-
trl25ps
6
4-
log Te
4-
(b)
I ________
20
40
60
1 09
02
80I
~
-__________ I
20 J__.
t
40
I
R lJ.Lm) Fig.
3(a). As in fig.
1(a) but at t
=
125 ps. (b) As in fig. 1(b) but at t
125 ps.
—
-
t
t =l9Ops
l9Ops
8—
8— Te
I
20I
40
I
RI,~m)
60I
I
6
Iog~
: ~ 0
I
logy 20
40I
R
Fig. 4. (a) As in fig. 1(a) but at t = 190 ps. (b) As in fig. 1(b) but at t = 190 Ps. 432
log Te
-
Log Tr
I 80
~—_._____........
~‘‘-_--~
6-
0
80
Rlj~m)
10 10
60 I log
60I
80
Volume hA, number 6
PHYSICS LETTERS
For theoretical purposes we have also studied the compression of the above target using laser pulses with pulse duration varied in the range 70 250 Ps while the total energy in the pulse is kept constant. The results are given in fig. 6. Further in fig. 7 we plot the results obtained by simulating the compression
io~’
-
23 June 1980
3 I
PC J/m
—
variedintherangel5—8Okg/m~wlu~chcorresponds to a pressure of 18 95 atmospheres at room temper. ature. The pulse parameters in this case are kept constant.
l2SPs
-
1O1z
SOps
-
so ps
-~-
-
0
10
3. Discussion of the results. As mentioned m the 10 previous section figs. 1(a) 4(a) characterise the im plosion scenario with radiation transport included in the code. It is seen from fig. 1(a) that within 50 Ps the ___________________________________ radiation temperature in the gas ahead of the compressed material rises from 5 X lO4K to 74 X 105K, the vertical line representing the gas-shell boundary. Consequently the electrons are heated by the radiation field and at this stage the electron temperature has increased from 5 X 104K to 6.8 X 1O4K. Further in figs. 2(a) and 3(a) the radiation temperature rises to I I I 106 and 1.3 X lO6K while the corresponding electron 0 20 40 temperature becomes 105K and 2.6 X 105K respectively. R I As a result of this preheat the inner pressure is increased before the target is compressed. Fig. 5 shows Fig. 5. Radial dependence of the target inner pressure at t = 0, the pressure history of the target at time t = 0, 50 80 50, 80 and 125 ps. and 125 Ps. It is seen that during this time the inner pressure increases from 6 X 108 JIm3 to 1010 J/m3 i.e. by a factor 17. The final compression plotted in fig. 4(a) shows on average a maximum gas density —7 X 1 o~ kg/rn3 and a maximum tamper density 00 —1.8 X i04 kg/m3. From fig. 4(b), however, we see that excluding the radiative transport, the target can 6 be compressed to a gas density —2 X lO~kg/m3 and Io~ a maximum shell density —10 5 kg/rn3. Thus radiative preheat can substantially degrade the compression of “ — the target. Fig. 6 shows log p and log Te versus r, keeping the laser pulse energy constant. Broken lines correspond 2 to inclusion of radiative transport; solid lines represent the case of no radiative transport. In the range r = 70 150 ps the final gas density increases steadily in both 200 250 cases. As r is varied from 150— 250 ps, the final density achieved in the case of no radiative transport decreases Fig. 6. Dependence of log p and log Te on r. radiation and then becomes constant. Including radiation effects transport included. radiation transport excluded. Energy on the other hand we fmd that the final density increases, absorbed = 7J. —
-______________________________
-
-
~
—
—
——
_—--.=-~.~-_---—-—
—
- - -
—
433
Volume 77A, number 6
PHYSICS LETTERS
6
Pg
Next in fig. 7 we plot maximum gas density p versus initial gas pressure of the gas in the target while the laser pulse parameters are kept constant at r = 100 Ps and ~m = 700 GW. The solid line in the graph shows that in the case of no radiative transport the maximum final gas density increases for Pg = 18 35 atm. This is due to minimization of shock heating. If the initial gas density is increased further the inner pressure becomes large enough to reduce the final compression. On the other hand the maximum achieved density remains almost constant when radiation effects~are in cluded. This is due to the fact that as ~ is increased the electron-ion and electron-radiation collision frequencies increase and the inner pressure rises more rapidly. This effect overshadows the decrease in shock heating.
-
log
23 June 1980
p
—-
-
-
10
I 30
I 50 Pg
I
I 70
I
I
J............j
IatiiiOs)
Fig. 7. Dependence of log p on Pg. ----radiation transport included. — radiation transport excluded. Energy absorbed = 7J. r = 100 ps. ~rn = 5.26 GW/steradian.
This phenomenon is due to radiation cooling of the target which takes place with longer laser pulses, as can be seen from the corresponding electron temperature curve in the same figure.
434
References
90 [1] N.A. Tahir, Rutherford Laboratory Annual Report (1979), RL-79-036. [21 N.A. Tahir and E.W. Laing, Plasma Physics (1979), submitted for publication. [3] J.P. Christiansen, D.E.T.F. Ashby and K.V. Roberts, Comp. Phys. Comm. 7 (1974) 271. [4] Y.B. Zel’dovich and Y.P. Raizer. Physics of shock waves
and high temperature phenomena (Academic Press, 1967). [5] R.G. Evans, Private communication. [6] E.W. Laing and N.A. Tahir, Rutherford Laboratory Annual Report (1978), RL-78-039.
PHYSICS LETFERS
23 June 1980
RADIATION EFFECTS IN GAS FILLED MICROBALLOONS N.A. TAHIR and E.W. LAING Department of Natural Philosophy, The University. Glasgow G12 8QQ, Scotland Received 1 February 1980
Using a modified form of the computer code MEDUSA we study the effect of radiative diffusion in laser compression simulations of neon filled, thin glass microballoons. Our calculations show that the radiative preheat of the target reduces 5 kg/rn3 to 1.8 x i04 kg/rn3. the final gas density by up to a factor 3 while the final shell density drops from i0
1. Introduction. In previous publications [1,21 we have discussed modifications to MEDUSA [3] a single velocity, two temperature 1-D Lagrangian computer code, by inclusion of a steady state radiation physics model. In this model the total continuum radiation arising from free-free and free.bound transitions diffuses 8-
into the medium in an assumed Planckian distribution
using the Rosseland mean opacity. Our calculations do not take account of line radiation effects. The Rosseland mean opacity for the total continuum radiation is evaluated in our calculations using a simple LIE hydrogenic approximation given by ref. [4]. Using 8
tr50ps
t~ 5Ops
log Te
log
logTr
__
Te
__
(a)
(b)
2-
2Logy
Log ~
_______________________________
0
20
40
R (j~ml
________________
60
0
20
I
40
I 60
R (,um)
Fig. 1. (a) Dependence of log ~, log Tr and log Te on target radius at t = 50 ps, radiation transport included. (b) Dependence of log p and log Te on target radius at t = 50 ps, radiation transport excluded.
430
Volume 77A, number 6
PHYSICS LETTERS
this modified version of the code we have carried out numerous computer runs to study the transport of continuum radiation in a neon filled thin glass microballoon. The object of these calculations is to investigate the preheat effect which arises from the penetration of the medium energy photons created at the critical density, into the uncompressed target core where they deposit their energy. We do not study the emission spectrum which would require a more sophisticated multigroup photon model. The laser pulse parameter used in these calculations are well within the capability of the Nd glass laser at the Central Laser Facility, Rutherford Laboratory. The target parameters are also chosen to match approximately targets used in a number of experiments performed at the Rutherford Laboratory Laser Division [5] -
2. Details of the problem. The target used in these calculations is a glass microballoon with inner radius R1 = 35 sum.. wall thickness L~R= 0.9 .tm and filled with neon at 18 atmospheres at room temperature i.e. at a 3. A Gaussian laser pulse with total density of 15 kg/m energy —~7OJ is used to compress this target. The peak power in the pulse ~m is —P700 GW and pulse duration, T, is lOOps. Experiments suggest that about 10% of 8
-
t:BOps
the laser energy is absorbed under these conditions and the remainder reflected. This partial absorption is treated in the code by inclusion of a factor in the absorption subroutine. No attempt is made to treat the reflection of the laser light. For comparison we have stimulated the compression of this target with and without radiative transport and the results are plotted in figs. 1—4. Figures labelled (a) correspond to inclusion of radiative transport while (b) denotes cases where radiation is excluded. In the latter case the energy is transported by a flux limited electron thermal conduction model, while in the former case both electron and radiation thermal conduction are considered. Flux limiting prevents the code from over-estimating the thermal flux in case of large temperature gradients. Also in the case of no radiative transport, radiation self absorption is considered in the overdense core region whereas in the underdense corona region the radiation is allowed to escape freely. The degree of ionization in the two cases is evaluated by a steady state density and temperature physics model which assumes thedependent plasma toatomic be in ionizational equiibrium due to a balance between collisional ionization + photoionization and three.body + radiative recombination [6]. 8
:: ::
23 June 1980
t:BOps
-
:—‘~
(~)
2~0’
(b)
______
logy 610
log
-
I
R(,um)
RçM.nl) Fig. 2. (a) As in fig. 1(a) but at r = 80 ps. (b) As in fig. 1(b) but at t
=
80 ps.
431
Volume 77A, number 6
8
6
PHYSICS LETTERS
-
8 t =125ps
-
Te log log Tr
23 June 1980
-
trl25ps
6
4-
log Te
4-
(b)
I ________
20
40
60
1 09
02
80I
~
-__________ I
20 J__.
t
40
I
R lJ.Lm) Fig.
3(a). As in fig.
1(a) but at t
=
125 ps. (b) As in fig. 1(b) but at t
125 ps.
—
-
t
t =l9Ops
l9Ops
8—
8— Te
I
20I
40
I
RI,~m)
60I
I
6
Iog~
: ~ 0
I
logy 20
40I
R
Fig. 4. (a) As in fig. 1(a) but at t = 190 ps. (b) As in fig. 1(b) but at t = 190 Ps. 432
log Te
-
Log Tr
I 80
~—_._____........
~‘‘-_--~
6-
0
80
Rlj~m)
10 10
60 I log
60I
80
Volume hA, number 6
PHYSICS LETTERS
For theoretical purposes we have also studied the compression of the above target using laser pulses with pulse duration varied in the range 70 250 Ps while the total energy in the pulse is kept constant. The results are given in fig. 6. Further in fig. 7 we plot the results obtained by simulating the compression
io~’
-
23 June 1980
3 I
PC J/m
—
variedintherangel5—8Okg/m~wlu~chcorresponds to a pressure of 18 95 atmospheres at room temper. ature. The pulse parameters in this case are kept constant.
l2SPs
-
1O1z
SOps
-
so ps
-~-
-
0
10
3. Discussion of the results. As mentioned m the 10 previous section figs. 1(a) 4(a) characterise the im plosion scenario with radiation transport included in the code. It is seen from fig. 1(a) that within 50 Ps the ___________________________________ radiation temperature in the gas ahead of the compressed material rises from 5 X lO4K to 74 X 105K, the vertical line representing the gas-shell boundary. Consequently the electrons are heated by the radiation field and at this stage the electron temperature has increased from 5 X 104K to 6.8 X 1O4K. Further in figs. 2(a) and 3(a) the radiation temperature rises to I I I 106 and 1.3 X lO6K while the corresponding electron 0 20 40 temperature becomes 105K and 2.6 X 105K respectively. R I As a result of this preheat the inner pressure is increased before the target is compressed. Fig. 5 shows Fig. 5. Radial dependence of the target inner pressure at t = 0, the pressure history of the target at time t = 0, 50 80 50, 80 and 125 ps. and 125 Ps. It is seen that during this time the inner pressure increases from 6 X 108 JIm3 to 1010 J/m3 i.e. by a factor 17. The final compression plotted in fig. 4(a) shows on average a maximum gas density —7 X 1 o~ kg/rn3 and a maximum tamper density 00 —1.8 X i04 kg/m3. From fig. 4(b), however, we see that excluding the radiative transport, the target can 6 be compressed to a gas density —2 X lO~kg/m3 and Io~ a maximum shell density —10 5 kg/rn3. Thus radiative preheat can substantially degrade the compression of “ — the target. Fig. 6 shows log p and log Te versus r, keeping the laser pulse energy constant. Broken lines correspond 2 to inclusion of radiative transport; solid lines represent the case of no radiative transport. In the range r = 70 150 ps the final gas density increases steadily in both 200 250 cases. As r is varied from 150— 250 ps, the final density achieved in the case of no radiative transport decreases Fig. 6. Dependence of log p and log Te on r. radiation and then becomes constant. Including radiation effects transport included. radiation transport excluded. Energy on the other hand we fmd that the final density increases, absorbed = 7J. —
-______________________________
-
-
~
—
—
——
_—--.=-~.~-_---—-—
—
- - -
—
433
Volume 77A, number 6
PHYSICS LETTERS
6
Pg
Next in fig. 7 we plot maximum gas density p versus initial gas pressure of the gas in the target while the laser pulse parameters are kept constant at r = 100 Ps and ~m = 700 GW. The solid line in the graph shows that in the case of no radiative transport the maximum final gas density increases for Pg = 18 35 atm. This is due to minimization of shock heating. If the initial gas density is increased further the inner pressure becomes large enough to reduce the final compression. On the other hand the maximum achieved density remains almost constant when radiation effects~are in cluded. This is due to the fact that as ~ is increased the electron-ion and electron-radiation collision frequencies increase and the inner pressure rises more rapidly. This effect overshadows the decrease in shock heating.
-
log
23 June 1980
p
—-
-
-
10
I 30
I 50 Pg
I
I 70
I
I
J............j
IatiiiOs)
Fig. 7. Dependence of log p on Pg. ----radiation transport included. — radiation transport excluded. Energy absorbed = 7J. r = 100 ps. ~rn = 5.26 GW/steradian.
This phenomenon is due to radiation cooling of the target which takes place with longer laser pulses, as can be seen from the corresponding electron temperature curve in the same figure.
434
References
90 [1] N.A. Tahir, Rutherford Laboratory Annual Report (1979), RL-79-036. [21 N.A. Tahir and E.W. Laing, Plasma Physics (1979), submitted for publication. [3] J.P. Christiansen, D.E.T.F. Ashby and K.V. Roberts, Comp. Phys. Comm. 7 (1974) 271. [4] Y.B. Zel’dovich and Y.P. Raizer. Physics of shock waves
and high temperature phenomena (Academic Press, 1967). [5] R.G. Evans, Private communication. [6] E.W. Laing and N.A. Tahir, Rutherford Laboratory Annual Report (1978), RL-78-039.