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Local velocity evaluation in a laser-produced plasma
Volume 105A, number 1,2
PHYSICS LETTERS
1 October 1984
LOCAL VELOCITY EVALUATION IN A LASER-PRODUCED PLASMA
Shizuyo HASHIMOTO Department of Physics, Faculty of Science, Tokai University, Hiratsuka, Kanagawa 259-12, Japan Received 30 September 1983
We show that the flight velocities in a laser-produced plasma at various distances from the target can be deduced from measured Doppler shifts of spectral self-reversal for the Be IV Ly-~ line with the help of a simple model. The red Starkshifts are taken into account.
The profiles of the Lyman-~ line emitted from laserproduced plasma at various distances (z) from a target show an asymmetric self-reversal near the center due to absorption by the cooler plasma in the peripheral region, as shown in fig. 1 for the Be IV L y ~ line. A method to extract the flight velocity of plasma perpenxX\
dicular to the target from the size of the measured asymmetric self-reversal is proposed by using a simple model. A high-density plasma was produced by using a 5 J mode-locked Nd-glass laser focused into a beryllium plane target in a vacuum chamber. The duration of the
/"
Be N 75928
o
\~
absorption
x I I/ I I I I I
z =0.00mm
0.14
- -
-0.2
0~
0.2 Z
Fig. 1. Profiles of the Be IV Ly-a line at various distances z from the target.
54
0.4
Volume 105A, number 1,2
PHYSICS LETTERS
laser pulse was 100 ps. The power density on the target surface is estimated to be 1014 W/cm 2. A 2 m grazing-incidence spectrograph equipped with a spatial resolving slit o f 100/~m width was used. The plasma was observed, for convenience, at an angle o f 20 ° from the plane target surface. For a complete and quantitative treatment of the shape of the observed profile, the equation o f radiative transfer must be solved with suitable modifications. TondeUo and Janitti et al. [1,2] have investigated broadening and self-absorption for the same line in a laser-produced plasma. They have estimated the shapes o f intensity profiles assuming a free-streaming o f the plasma with constant absolute velocities distributed over a solid angle. In order to'solve the radiative transfer equation exactly, many assumptions must be made for many unknown parameters, such as: spatial distribution o f electron density, electron and ion temperature, population density distribution among the upper levels and the ground level, and geometrical depth of plasma etc. In the present investigation, instead o f solving the equation exactly, the total absorption profile and the corrected profde which are integrated along the path of observation are obtained by assuming that both profiles have lorenzian shapes except for the wing ,1, since the thermal Doppler width is much smaller than the Stark width. The derived absorption prot'fles at various distances from the target are shown in fig. 1 at ,1 The wings of line-profile of the Be IV Ly-a line showed asymmetry, because some satellite lines arising from transitions of helium-like doubly excited states (lsnl-2pnl)were superposed on a red wing.
1 October 1984
the top. In fig. 1, the position o f the origin A)~ = 0 for each profile at z = 0.14 mm and 0.28 mm was determined by bisecting the line profile at various intensities without using the central region. The position o f the origin at z = 0.00 mm was determined from the position o f the line center at z = 0.14 m m (cf. ref. [3] for details). One can see that the peak positions of absorption profiles in these figures are all shifted more or less towards the blue. The measured sizes o f these shifts are listed in the second column o f table 1. These mean that absorbing particles at each distance had macroscopically larger velocity components in the direction o f observation than that o f the emitting particles, the differences of which are listed in the third column of the same table. We have measured a rather large red Stark shift of the line center at a distance close to a target, as reported in a previous report [3]. The present size o f the Doppler shift close to the target surface is about one order o f magnitude smaller than that estimated by Jannitti et al. [2]. They have taken the total shifts (IAXDsl + IAX Stark[) shown in the inset in fig. 1 as Doppler shift. In order to deduce the velocities of emitting particles in the z direction at various distances from the observed Doppler shifts o f reabsorption peak, the following simple model was used. The emitting hot plasma is assumed to expand in a cone shown by the hatching in fig. 2. The vertical angle o f this cone 201 is assumed to be 15 °, deduced from the observation by using a spatial resolving slit o f the spectrograph which was set parallel to the z-axis. The expansion velocities were assumed to depend on directional angle 0, i.e., V 2 = a b sec 0, where a and b are suitable constants witha
-
Table 1 Observed Doppler shifts of self-reversal for the Be IV Ly-a line with the corresponding velocity differences AV~ and the computed flight velocities of the plasma along the target normal at various distances from the target. Vl, V2 and Va are three examl~les of particle velocities corresponding to 3 different angular distributons, c is a proportiona~tY constant, cV~ = 3 - 2 see 0, cV~ = 4 - 3 sec 0, cV] = 5 - 4 sec0, Vl(O)/-~ = 5.58, V2(0)/~-~ = 9.69, V3(0)/AV~ = 8.31 Observed
Calculated
z (mm)
AhDs (A)
AV~ (cm/s)
Vx(O,z)(cm/s)-
V2(0, z) (cm/s)
Vz(0, z)(cm/s)
0.00 0.14 0.28
-0.003 ± 0.002 -0.005 ± 0.002 -0.015 ± 0.002
(1.2 ± 0.8) X 10 6 (2.0 ± 0.8) × 106 (6.0 ± 0.8) X 106
(0.7 ± 0.4) X 10 7 (1.1 ± 0.4) X 107 (3.3 +_0.4) X 107
(0.8 ± 0.5) X 10 7 (1.4 ± 0.5) X 107 (4.2 ± 0.5) X 107
(1.0 ± 0.7) X 107 (1.7 ± 0.7) X 107 (5.0 ± 0.7) X 107
55
Volume 105A, number 1,2
PHYSICS LETTERS
/
go is the
S--'/~''."''.'. . -
1 October 1984
.
.
~
.
•
• .
~.
"
.~
number of absorbing particles which is proportional to (0 c - 0). The observed Doppler shift of the reabsorption peak is considered to be due to the mean velocity difference
Laser
•
(
AV~ = 17s - Vs, .........
I
.
.
.
.
.
.
.
.
.
v(o)
where
.
Vs(O')
01
V(O')
-
Vs = to s p e c t r o g r a p h
> b. Three pairs of examples (see table 1) were taken by referring to the shape o f the crater which was left on the target surface by ablation. In fig. 2, Vs(0 ) represents the velocity component in the direction-ofsight o f V(O) for an emitting particle, i.e.,
V(O) cos(70 °
- O)
= X/s - b sec 0 cos(V0 ° - 0 ) ,
0 c 0z' 1
v; -
f f 0
2o Vs(O,o') dOdO',
-01
where 01
G=f --01
56
go dO
f
Vs(O)dO.
o
The ratios of V(0)/Al,7~have been computed for three pairs of parameters a and b, and for 01 = 7.5 °, as in the equations in the caption of table 1. By using these ratios, velocities in the direction of the z-axis at vari___ous distances, V(0,z); are derived from the values of AVe(z) and shown in the third column o f table I. It can be seen from these results that the velocities of flight of the plasma increase as z increases. The calculat. ed result of V 3 at z = 0.28 m m agrees with the macroscopically measured result of 5 X 107 cm/s obtained with the time-of-flight method.
(1)
and Vs(O') represents that for an absorbing particle. The light emitted by a particle which expands in the direction 0 is assumed to be absorbed by particles expanding in the direction 0' with 0 < 0' < Oc, where 0 c is the critical angle at which V'(O) becomes zero. The difference between the velocity components Vs(O') and Vs(0 ) will contribute to the Doppler shift of the reabsorption peak. By integrating these differences twice, with respect to absorbing particles and emitting particles, from 0 to 0 c and from - 0 1 to +01 respectively (see fig. 2), the weighted mean velocity component 17~ is calculated to be --r
1
--01
Fig. 2. Simplified model of the plasma structure. The hatched area shows the emitting hot plasma region and the dotted area shows the absorbing cooler plasma region.
Vs(O ) =
(3)
(2)
The author wishes to thank Dr. N. Yamaguchi for his collaboration in the experiments. This work was carried out under the Collaborating Research Program at Institute of Plasma Physics, Nagoya University, Nagoya, Japan.
References [ 1] G. Tondello, E. Jannitti and M. Malvezzi, Phys. Rev. A16 (1977) 1705. [2] E. Jannitti, P. Nicolosi, G. Tondello, L. Garifo and A.M. Malvezzi, in: Laser interaction and related plasma phenomena, Vol. 4A (Plenum, New York, 1977) p. 387. [3] S. Hashimoto and N. Yamaguchi, Phys. Lett. 95A (1983) 299.
PHYSICS LETTERS
1 October 1984
LOCAL VELOCITY EVALUATION IN A LASER-PRODUCED PLASMA
Shizuyo HASHIMOTO Department of Physics, Faculty of Science, Tokai University, Hiratsuka, Kanagawa 259-12, Japan Received 30 September 1983
We show that the flight velocities in a laser-produced plasma at various distances from the target can be deduced from measured Doppler shifts of spectral self-reversal for the Be IV Ly-~ line with the help of a simple model. The red Starkshifts are taken into account.
The profiles of the Lyman-~ line emitted from laserproduced plasma at various distances (z) from a target show an asymmetric self-reversal near the center due to absorption by the cooler plasma in the peripheral region, as shown in fig. 1 for the Be IV L y ~ line. A method to extract the flight velocity of plasma perpenxX\
dicular to the target from the size of the measured asymmetric self-reversal is proposed by using a simple model. A high-density plasma was produced by using a 5 J mode-locked Nd-glass laser focused into a beryllium plane target in a vacuum chamber. The duration of the
/"
Be N 75928
o
\~
absorption
x I I/ I I I I I
z =0.00mm
0.14
- -
-0.2
0~
0.2 Z
Fig. 1. Profiles of the Be IV Ly-a line at various distances z from the target.
54
0.4
Volume 105A, number 1,2
PHYSICS LETTERS
laser pulse was 100 ps. The power density on the target surface is estimated to be 1014 W/cm 2. A 2 m grazing-incidence spectrograph equipped with a spatial resolving slit o f 100/~m width was used. The plasma was observed, for convenience, at an angle o f 20 ° from the plane target surface. For a complete and quantitative treatment of the shape of the observed profile, the equation o f radiative transfer must be solved with suitable modifications. TondeUo and Janitti et al. [1,2] have investigated broadening and self-absorption for the same line in a laser-produced plasma. They have estimated the shapes o f intensity profiles assuming a free-streaming o f the plasma with constant absolute velocities distributed over a solid angle. In order to'solve the radiative transfer equation exactly, many assumptions must be made for many unknown parameters, such as: spatial distribution o f electron density, electron and ion temperature, population density distribution among the upper levels and the ground level, and geometrical depth of plasma etc. In the present investigation, instead o f solving the equation exactly, the total absorption profile and the corrected profde which are integrated along the path of observation are obtained by assuming that both profiles have lorenzian shapes except for the wing ,1, since the thermal Doppler width is much smaller than the Stark width. The derived absorption prot'fles at various distances from the target are shown in fig. 1 at ,1 The wings of line-profile of the Be IV Ly-a line showed asymmetry, because some satellite lines arising from transitions of helium-like doubly excited states (lsnl-2pnl)were superposed on a red wing.
1 October 1984
the top. In fig. 1, the position o f the origin A)~ = 0 for each profile at z = 0.14 mm and 0.28 mm was determined by bisecting the line profile at various intensities without using the central region. The position o f the origin at z = 0.00 mm was determined from the position o f the line center at z = 0.14 m m (cf. ref. [3] for details). One can see that the peak positions of absorption profiles in these figures are all shifted more or less towards the blue. The measured sizes o f these shifts are listed in the second column o f table 1. These mean that absorbing particles at each distance had macroscopically larger velocity components in the direction o f observation than that o f the emitting particles, the differences of which are listed in the third column of the same table. We have measured a rather large red Stark shift of the line center at a distance close to a target, as reported in a previous report [3]. The present size o f the Doppler shift close to the target surface is about one order o f magnitude smaller than that estimated by Jannitti et al. [2]. They have taken the total shifts (IAXDsl + IAX Stark[) shown in the inset in fig. 1 as Doppler shift. In order to deduce the velocities of emitting particles in the z direction at various distances from the observed Doppler shifts o f reabsorption peak, the following simple model was used. The emitting hot plasma is assumed to expand in a cone shown by the hatching in fig. 2. The vertical angle o f this cone 201 is assumed to be 15 °, deduced from the observation by using a spatial resolving slit o f the spectrograph which was set parallel to the z-axis. The expansion velocities were assumed to depend on directional angle 0, i.e., V 2 = a b sec 0, where a and b are suitable constants witha
-
Table 1 Observed Doppler shifts of self-reversal for the Be IV Ly-a line with the corresponding velocity differences AV~ and the computed flight velocities of the plasma along the target normal at various distances from the target. Vl, V2 and Va are three examl~les of particle velocities corresponding to 3 different angular distributons, c is a proportiona~tY constant, cV~ = 3 - 2 see 0, cV~ = 4 - 3 sec 0, cV] = 5 - 4 sec0, Vl(O)/-~ = 5.58, V2(0)/~-~ = 9.69, V3(0)/AV~ = 8.31 Observed
Calculated
z (mm)
AhDs (A)
AV~ (cm/s)
Vx(O,z)(cm/s)-
V2(0, z) (cm/s)
Vz(0, z)(cm/s)
0.00 0.14 0.28
-0.003 ± 0.002 -0.005 ± 0.002 -0.015 ± 0.002
(1.2 ± 0.8) X 10 6 (2.0 ± 0.8) × 106 (6.0 ± 0.8) X 106
(0.7 ± 0.4) X 10 7 (1.1 ± 0.4) X 107 (3.3 +_0.4) X 107
(0.8 ± 0.5) X 10 7 (1.4 ± 0.5) X 107 (4.2 ± 0.5) X 107
(1.0 ± 0.7) X 107 (1.7 ± 0.7) X 107 (5.0 ± 0.7) X 107
55
Volume 105A, number 1,2
PHYSICS LETTERS
/
go is the
S--'/~''."''.'. . -
1 October 1984
.
.
~
.
•
• .
~.
"
.~
number of absorbing particles which is proportional to (0 c - 0). The observed Doppler shift of the reabsorption peak is considered to be due to the mean velocity difference
Laser
•
(
AV~ = 17s - Vs, .........
I
.
.
.
.
.
.
.
.
.
v(o)
where
.
Vs(O')
01
V(O')
-
Vs = to s p e c t r o g r a p h
> b. Three pairs of examples (see table 1) were taken by referring to the shape o f the crater which was left on the target surface by ablation. In fig. 2, Vs(0 ) represents the velocity component in the direction-ofsight o f V(O) for an emitting particle, i.e.,
V(O) cos(70 °
- O)
= X/s - b sec 0 cos(V0 ° - 0 ) ,
0 c 0z' 1
v; -
f f 0
2o Vs(O,o') dOdO',
-01
where 01
G=f --01
56
go dO
f
Vs(O)dO.
o
The ratios of V(0)/Al,7~have been computed for three pairs of parameters a and b, and for 01 = 7.5 °, as in the equations in the caption of table 1. By using these ratios, velocities in the direction of the z-axis at vari___ous distances, V(0,z); are derived from the values of AVe(z) and shown in the third column o f table I. It can be seen from these results that the velocities of flight of the plasma increase as z increases. The calculat. ed result of V 3 at z = 0.28 m m agrees with the macroscopically measured result of 5 X 107 cm/s obtained with the time-of-flight method.
(1)
and Vs(O') represents that for an absorbing particle. The light emitted by a particle which expands in the direction 0 is assumed to be absorbed by particles expanding in the direction 0' with 0 < 0' < Oc, where 0 c is the critical angle at which V'(O) becomes zero. The difference between the velocity components Vs(O') and Vs(0 ) will contribute to the Doppler shift of the reabsorption peak. By integrating these differences twice, with respect to absorbing particles and emitting particles, from 0 to 0 c and from - 0 1 to +01 respectively (see fig. 2), the weighted mean velocity component 17~ is calculated to be --r
1
--01
Fig. 2. Simplified model of the plasma structure. The hatched area shows the emitting hot plasma region and the dotted area shows the absorbing cooler plasma region.
Vs(O ) =
(3)
(2)
The author wishes to thank Dr. N. Yamaguchi for his collaboration in the experiments. This work was carried out under the Collaborating Research Program at Institute of Plasma Physics, Nagoya University, Nagoya, Japan.
References [ 1] G. Tondello, E. Jannitti and M. Malvezzi, Phys. Rev. A16 (1977) 1705. [2] E. Jannitti, P. Nicolosi, G. Tondello, L. Garifo and A.M. Malvezzi, in: Laser interaction and related plasma phenomena, Vol. 4A (Plenum, New York, 1977) p. 387. [3] S. Hashimoto and N. Yamaguchi, Phys. Lett. 95A (1983) 299.