- Email: [email protected]
High density plasma physics with heavy-ion beams
Nuclear Instruments and Methods in Physics Research A 415 (1998) 61—67
High density plasma physics with heavy-ion beams S. Sto¨we!,*, R. Bock!, M. Dornik!, P. Spiller!, M. Stetter!, V.E. Fortov", V. Mintsev", M. Kulish", A. Shutov", V. Yakushev", B. Sharkov#, S. Golubev#, B. Bruynetkin#, U. Funk$, M. Geissel$, D.H.H. Hoffmann$, N.A. Tahir$ ! GSI-Darmstadt, Planckstrassc 1, D-64291 Darmstadt, Germany " Institute of Chemical Physics,142432 Chernogolovka, Moscow Region, Russia # Institute of Theoretical and Experimental Physics, 117259 Moscow, Russia $ Universita( t Erlangen, Erwin-Rommelstr. 1, D-91085 Erlangen, Germany
Abstract The accelerator facilities at GSI Darmstadt offer a unique possibility for experiments with heavy-ion-induced dense plasmas. Although the intensity of these heavy-ion beams is far below the regime of ICF, such beams are used to study basic physics, to develop diagnostic tools and special heavy-ion target designs. During the last years hydrodynamic motion has been induced for the first time in cryogenic crystals and metal targets by stopping intense heavy-ion beams. In recent experiments at the High Density Target Area a maximum specific energy deposition of 1 kJ/g in an initially solid lead target was reached. The time and spatial development of the hydrodynamic expansion after the heating phase and the propagation of pressure waves in the target were measured. The experimental results are compared with the results of a 2-D hydrodynamic code. ( 1998 Elsevier Science B.V. All rights reserved.
1. Introduction Intense relativistic heavy-ion beams are an excellent tool to generate dense plasmas. The main feature of this scheme is the direct coupling of the beam energy into matter over a range of several millimeters. This opens up the possibility of heating rather large volumes of matter at solid-state density, typically of the order of a few cubic millimeters. Experiments in fundamental research on the equation of state of matter, phase transitions
* Corresponding author. Tel.: #49 6149 712293; fax: #49 6159 712992; e-mail: [email protected].
and opacities will be possible. This knowledge is of considerable interest in the field of astrophysics, geophysics, and inertial confinement fusion (ICF). One of the main topics of the plasma physics research at the Gesellschaft fu¨r Schwerionenforschung mbH (GSI) is the diagnostics of dense plasmas generated by the impact of relativistic heavy ions in solid targets. The heavy-ion synchrotron SIS can accelerate even heaviest projectiles, like Uranium up to energies of 1 GeV per nucleon. For the issues of heavy-ion induced plasmas, the use of an Argon beam with an energy of 300 MeV per nucleon turned out to be the most effective way (at present GSI conditions) to achieve a high specific energy deposition (E ) in a solid target. S
0168-9002/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 8 ) 0 0 5 0 8 - 7
I. OVERVIEWS
62
S. Sto( we et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 61—67
The beam, extracted from the SIS, is guided to the High Density Target Area. During the last three years a lot of effort was put into increasing the specific energy deposition (E ) of the ions. The main S issues for the enhancement of E are the reduction S of the focal spot size, the increase in number of projectiles and the reduction of beam pulse length. With the improvement in all three parameters and using the enhanced energy deposition at the end of the ion range, the so-called Bragg peak, we reach now an energy deposition of 1 kJ/g in a solid lead target. The specific energy deposition determines the thermodynamic parameters of the heated matter. The expected temperature immediately after the heating phase is 0.2 eV, the pressure is in the range of 2—4 GPa and the density is close to that in the solid state. In recent experiments it was possible for the first time to observe the hydrodynamic motion of heavyion heated metal. The expansion can be examined from 2-D frames obtained by time-resolved optical shadowgraphy. The propagation and amplitude of pressure waves through the target, are detected with piezo-electric pressure gauges. Apart from solid metal targets, cryogenic gas targets, i.e. solid xenon, krypton [1], argon, neon and ultimately hydrogen are objects of our research. Because of the low cohesive energy of these
cryogenic solids, it is possible to observe hydrodynamic motion even at a quite low energy deposition. Due to the transparency of the targets for visible light, spectroscopic methods for the investigation of the beam—target interaction zone can be used. A high compression of a cryogenic target, which is of special importance for ICF research, can be reached by the use of an indirectly driven target. The idea of such a new target design and an estimation of the plasma parameters are treated in the paper by Funk [2].
2. The High Density Target Area The experimental activities of the GSI plasma physics group described in this publication are carried out at the High Density Target Area. The main components of the target area are a plasma lens final focusing system, a target vacuum chamber and a beam and plasma diagnostic setup (Fig. 1). The plasma lens is used for the reduction of the focal spot size of the heavy-ion beam by a factor of two compared to conventional quadrupole focusing. Focusing angles up to 90 mrad are provided by the plasma lens. The lens aberrations are low, so that the beam intensity distribution in the focal plane is determined by the beam emittance [3]. The
Fig. 1. Experimental setup at the High Density Target Area.
S. Sto( we et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 61—67
63
Fig. 2. Time structure of the SIS beam and improvements from 1996 to 1997.
transversal beam intensity profile has a Gaussian shape. Due to the different beam emittances in vertical and horizontal direction, the transversal distribution has an elliptical shape. The corresponding beam radii are 300 lm (sigma vertical) and 540 lm (sigma horizontal). The beam profile in the focal plane of the lens is measured by the light emission of a scintillator, which is observed with a gated CCD-camera. The pulse structure and absolute beam intensity are recorded with a fast current transformer. The recent experiments profit from an increase in beam intensity by a factor of four compared to experiments in 1996. The progress was made by the use of a MUCIS ion source, providing higher injection currents for the SIS. Now it is possible to heat the target with up to 2]1010 projectiles (40Ar18`300 MeV per Nucleon). The ions are delivered in a single beam bunch, which has a pulse length of 250 ns (FWHM). In former experiments the beam time structure was different. Four beam bunches, each 80 ns (FWHM) long, reached the target area. The bunch-to-bunch time distance was 270 ns. Fig. 2 shows the measured shape and amplitudes of the Argon beam pulses in 1996 and in the recent experiments. The reduction in total pulse length is important, in order to have no significant expansion of the heated matter during the heating phase. For the actual beam parameters this expansion is negligible. During the target heating time, which is equal to the pulse length of the beam (thermalization is several orders of magnitude fas-
Fig. 3. Specific energy deposition along the beam axis in a lead target, width of transversal beam intensity distribution versus penetration depth.
ter), the density of the matter stays constant. The range does not change significantly in comparison to the solid lead target, where the ions have a penetration depth of 11 mm. The spatial distribution of the specific energy deposition is determined by the shape of the beam envelope. The energy loss dE/dx increases with the penetration depth of the ions in the target. To calculate the deposition at the location of the Bragg peak, energy spread, energy loss straggling and angular straggling of the ions have to be taken into account. Fig. 3 shows the calculated longitudinal profile of the deposited energy at the position of the beam axis assuming constant density. In the lower part of the diagram, the beam envelope is plotted. The targets are mounted in a vacuum chamber. Using a high precision vacuum feedthrough, it is possible to adjust each target with respect to the beam axis. Two different geometries are used for the experiments with lead targets. The first configuration is a lead sheet of 1 mm thickness (Fig. 4a). The hydrodynamic motion of the heated target matter can be observed with a fast multiframing camera [4] and an optical backlighter. The direction of observation (x in Fig. 1) is perpendicular to the beam direction (z) and parallel to the surface of the lead sheet. The target is illuminated from the rear side with a xenon flash lamp. The shadow of the expanding matter is recorded with the camera.
I. OVERVIEWS
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S. Sto( we et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 61—67
The method, called time-resolved shadowgraphy, visualizes the hydrodynamic processes in 60 frames with a minimum interframing time of 1.7 ls. The second configuration consists of a lead cylinder, with implemented piezoelectric pressure gauges (Fig. 4b). The lead cylinder has a diameter of 17 mm, resulting in large volume of not directly heated matter around the interaction zone in comparison to the first target configuration. The gauges
are foils of polyvinylidene flouride (PVDF) with 25 lm thickness [5], having an active area of 5 mm2 and a sensitivity of 25 pC/N. The radial distance of the gauges to the beam axis is between 4 and 6 mm. The pressure wave passing the gauge causes a current signal in the electrical circuit of the gauges, which is recorded with a fast storage oscilloscope. The integrated signal is a measure of the pressure development with time. From the measured propagation time and amplitude, conclusions on the initial pressure conditions of the heated matter at the beam axis can be drawn.
3. Hydrodynamic response of heavy ion heated lead targets
Fig. 4. Lead-target geometry; (a) lead sheet (b) lead cylinder with implemented gauge.
In July 1997 first experiments to investigate the hydrodynamic response of a heavy-ion heated lead target were carried out. The lead sheet target configuration, described in the previous chapter (Fig. 4a), was adjusted in a way, that the focal plane of the plasma lens lies at the position of the Bragg peak inside the lead target. The beam axis coincides with the middle of the lead sheet. Fig. 5 shows six different frames, which show the expansion of the target at different time stages. The exposure time of
Fig. 5. Hydrodynamic expansion of a 1 mm thick lead sheet. s: shadow of solid lead, which was piled up in a previous shot at a different x-position on the sheet
S. Sto( we et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 61—67
65
4. Computer simulations of the hydrodynamic expansion
Fig. 6. Signal of two piezo-electric pressure gauges. The time resolution due to the thickness of the gauge is 10 ns.
each frame is 3.5 ls. The expansion of the lead in transversal direction is symmetric to the beam axis and the velocity of the material remains constant during the observation time of 40 ls. The vertical expansion velocity at the target entrance is 230$20 m/s. The velocity increases with the penetration depth of the ions in the target. At the location of the Bragg peak it reaches a maximum of 290 $20 m/s. The velocity of the matter, which is ejected from the target in longitudinal direction, has the reverse sign of the projectile velocity. The front of the expanding matter propagates with a speed of 210$30 m/s at the beam axis. Using the second target configuration it is possible to measure the shape and amplitude of pressure waves, which propagate from the beam—target interaction zone to outer target regions. Fig. 6 shows the pressure—time development, recorded with two gauges. Gauge 1 has a distance of 6 mm to the beam axis, gauge 2 a distance of 4 mm. The corresponding amplitudes are 0.16 GPa for gauge 1 and 0.10 GPa for gauge 2. The shape of the pressure pulse can be explained by the beam pulse structure, which is represented by the dashed curve (intensity in a.u.) and by the spatial beam intensity profile. No shockwave-like sharp pressure rise can be observed. The maximum of the pressure pulse propagates with 1.9$0.1 km/s through the observed radial region (4—6 mm), which is close to the sound velocity in lead [6].
In collaboration with the Institute of Chemical Physics (ICP) in Chernogolovka numerical simulations are carried out to understand the beam-target interaction and hydrodynamic phenomena. With the simulation it is possible to calculate the specific energy deposition in the target, taking into account the expansion of the matter, i.e. the change in density. The simulations are carried out with a 2-D hydrodynamic code, which treats interfaces with the Godunov method in moving grids [7]. The code uses a semi-empirical wide range equation of state [8]. The beam parameters such as beam envelope, energy and pulse shape are adapted to match the experimental data. The specific energy deposition is computed using the stopping power tables by Biersack and Ziegler [9]. One possible check for the simulation is a comparison with the pressure development in time, as measured with the piezoelectric gauges. The data of the simulation, which correspond to the experimental result in Fig. 6 are plotted in Fig. 7. The calculation is done in the plane, which is perpendicular to the beam axis at a penetration depth of 6 mm. The shape of the positive pressure pulse fits the experimental data well. The pulse amplitudes are 0.34 GPa (gauge 1) and 0.19 GPa (gauge 2) and thus by a factor of two higher than in the experiment. We assume, that this deviation is caused by the implementation of the gauges in a thin layer of
Fig. 7. Simulated pressure—time development at the position of the gauges.
I. OVERVIEWS
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S. Sto( we et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 61—67
Fig. 8. Energy, density, pressure and temperature distribution after 1200 ns, simulated with a 2-D hydrodynamic code.
Fig. 9. Temperature and density of heavy-ion-induced plasmas at GSI.
epoxy glue. This layer of a matter with lower acoustic impedance than lead is not taken into account in the calculation, which yields only the pressure in an infinite lead cylinder. The reason for the deviation in the arrival time of the pulses is the accuracy in
the experimental determination of the transversal gauge position with respect to the beam. Behind the positive pressure pulse, an expansion wave with negative pressures propagates through the target. This phenomenon, which is caused by the cohesive
S. Sto( we et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 61—67
forces in the dense matter, is not observed in the experiment. There is no explanation up to now, why this negative pulse is not recorded by the pressure gauges. A simulation with the same input parameters is carried out in a plane, which contains the beam axis. Cylindrical symmetry is assumed. Fig. 8. shows energy, pressure, density and temperature distribution in the lead target at a time of 1200 ns, which is 600 ns after the end of the heating phase. The range of the ions during the heating phase is not significantly enlarged by the dilution of the matter in the interaction zone. The maximum temperatures (2800 K) and pressures (3.8 GPa) are reached at t"400 ns in the center of the Bragg peak.
5. Conclusions and outlook The research in heavy-ion induced dense plasmas will benefit from the high intensity upgrade of the GSI accelerator facilities, which will be completed in 1999. The total kinetic beam energy will be in the range of 1 kJ, which is two orders of magnitude higher than the present beam energy. The pulse length of the beam is expected to be lower than 100 ns. This upgrade will lead to a specific energy deposition of more than 100 kJ/g and temperatures
67
between 1 and 10 eV at almost solid-state densities [10], enabling interesting experiments in the regime of non-ideal plasmas. Fig. 9 shows the parameter region, i.e. density and temperature of the target plasma, which are achievable with the present setup and after the upgrade 1999. In addition, the regions of different fusion plasmas are drawn: The sun, a magnetic fusion plasma, a converter plasma in an ICF-facility and the fuel of an ICF-pellet after compression are given as reference points on this “map”. References [1] [2] [3] [4] [5] [6]
[7] [8] [9] [10]
M. Dornik, Fusion Eng. and Des. 32—33 (1996) 511. U.N. Funk, Nucl. Instr. and Meth. A 415 (1998) 68. M. Stetter, Fusion Eng. and Des. 32—33 (1996) 503. Operation Manual of the VFU-1 Camera, ITEP Moscow, 1980 (in Russian). M. Boustie, Laser and Particle Beams 14 (2) (1996) 171. Zelkovich Raiser, Physics of Shockwaves and High-Temperature Hydrodynamic Phenomena II, Academic Press, New York, 1967, 698. V.E. Fortov, Nucl. Sci. and Eng. 123 (1996) 169. A.V. Bushman, Intense Dynamic Loading of Condensed Matter, Taylor & Francis, London, 1992. J.F. Ziegler, The Stopping and Range of Ions in Matter, vol. 1, Pergamon, Oxford, 1985. R.W. Mu¨ller, GSI-Report-96-07, Darmstadt, 1996.
I. OVERVIEWS
High density plasma physics with heavy-ion beams S. Sto¨we!,*, R. Bock!, M. Dornik!, P. Spiller!, M. Stetter!, V.E. Fortov", V. Mintsev", M. Kulish", A. Shutov", V. Yakushev", B. Sharkov#, S. Golubev#, B. Bruynetkin#, U. Funk$, M. Geissel$, D.H.H. Hoffmann$, N.A. Tahir$ ! GSI-Darmstadt, Planckstrassc 1, D-64291 Darmstadt, Germany " Institute of Chemical Physics,142432 Chernogolovka, Moscow Region, Russia # Institute of Theoretical and Experimental Physics, 117259 Moscow, Russia $ Universita( t Erlangen, Erwin-Rommelstr. 1, D-91085 Erlangen, Germany
Abstract The accelerator facilities at GSI Darmstadt offer a unique possibility for experiments with heavy-ion-induced dense plasmas. Although the intensity of these heavy-ion beams is far below the regime of ICF, such beams are used to study basic physics, to develop diagnostic tools and special heavy-ion target designs. During the last years hydrodynamic motion has been induced for the first time in cryogenic crystals and metal targets by stopping intense heavy-ion beams. In recent experiments at the High Density Target Area a maximum specific energy deposition of 1 kJ/g in an initially solid lead target was reached. The time and spatial development of the hydrodynamic expansion after the heating phase and the propagation of pressure waves in the target were measured. The experimental results are compared with the results of a 2-D hydrodynamic code. ( 1998 Elsevier Science B.V. All rights reserved.
1. Introduction Intense relativistic heavy-ion beams are an excellent tool to generate dense plasmas. The main feature of this scheme is the direct coupling of the beam energy into matter over a range of several millimeters. This opens up the possibility of heating rather large volumes of matter at solid-state density, typically of the order of a few cubic millimeters. Experiments in fundamental research on the equation of state of matter, phase transitions
* Corresponding author. Tel.: #49 6149 712293; fax: #49 6159 712992; e-mail: [email protected].
and opacities will be possible. This knowledge is of considerable interest in the field of astrophysics, geophysics, and inertial confinement fusion (ICF). One of the main topics of the plasma physics research at the Gesellschaft fu¨r Schwerionenforschung mbH (GSI) is the diagnostics of dense plasmas generated by the impact of relativistic heavy ions in solid targets. The heavy-ion synchrotron SIS can accelerate even heaviest projectiles, like Uranium up to energies of 1 GeV per nucleon. For the issues of heavy-ion induced plasmas, the use of an Argon beam with an energy of 300 MeV per nucleon turned out to be the most effective way (at present GSI conditions) to achieve a high specific energy deposition (E ) in a solid target. S
0168-9002/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 8 ) 0 0 5 0 8 - 7
I. OVERVIEWS
62
S. Sto( we et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 61—67
The beam, extracted from the SIS, is guided to the High Density Target Area. During the last three years a lot of effort was put into increasing the specific energy deposition (E ) of the ions. The main S issues for the enhancement of E are the reduction S of the focal spot size, the increase in number of projectiles and the reduction of beam pulse length. With the improvement in all three parameters and using the enhanced energy deposition at the end of the ion range, the so-called Bragg peak, we reach now an energy deposition of 1 kJ/g in a solid lead target. The specific energy deposition determines the thermodynamic parameters of the heated matter. The expected temperature immediately after the heating phase is 0.2 eV, the pressure is in the range of 2—4 GPa and the density is close to that in the solid state. In recent experiments it was possible for the first time to observe the hydrodynamic motion of heavyion heated metal. The expansion can be examined from 2-D frames obtained by time-resolved optical shadowgraphy. The propagation and amplitude of pressure waves through the target, are detected with piezo-electric pressure gauges. Apart from solid metal targets, cryogenic gas targets, i.e. solid xenon, krypton [1], argon, neon and ultimately hydrogen are objects of our research. Because of the low cohesive energy of these
cryogenic solids, it is possible to observe hydrodynamic motion even at a quite low energy deposition. Due to the transparency of the targets for visible light, spectroscopic methods for the investigation of the beam—target interaction zone can be used. A high compression of a cryogenic target, which is of special importance for ICF research, can be reached by the use of an indirectly driven target. The idea of such a new target design and an estimation of the plasma parameters are treated in the paper by Funk [2].
2. The High Density Target Area The experimental activities of the GSI plasma physics group described in this publication are carried out at the High Density Target Area. The main components of the target area are a plasma lens final focusing system, a target vacuum chamber and a beam and plasma diagnostic setup (Fig. 1). The plasma lens is used for the reduction of the focal spot size of the heavy-ion beam by a factor of two compared to conventional quadrupole focusing. Focusing angles up to 90 mrad are provided by the plasma lens. The lens aberrations are low, so that the beam intensity distribution in the focal plane is determined by the beam emittance [3]. The
Fig. 1. Experimental setup at the High Density Target Area.
S. Sto( we et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 61—67
63
Fig. 2. Time structure of the SIS beam and improvements from 1996 to 1997.
transversal beam intensity profile has a Gaussian shape. Due to the different beam emittances in vertical and horizontal direction, the transversal distribution has an elliptical shape. The corresponding beam radii are 300 lm (sigma vertical) and 540 lm (sigma horizontal). The beam profile in the focal plane of the lens is measured by the light emission of a scintillator, which is observed with a gated CCD-camera. The pulse structure and absolute beam intensity are recorded with a fast current transformer. The recent experiments profit from an increase in beam intensity by a factor of four compared to experiments in 1996. The progress was made by the use of a MUCIS ion source, providing higher injection currents for the SIS. Now it is possible to heat the target with up to 2]1010 projectiles (40Ar18`300 MeV per Nucleon). The ions are delivered in a single beam bunch, which has a pulse length of 250 ns (FWHM). In former experiments the beam time structure was different. Four beam bunches, each 80 ns (FWHM) long, reached the target area. The bunch-to-bunch time distance was 270 ns. Fig. 2 shows the measured shape and amplitudes of the Argon beam pulses in 1996 and in the recent experiments. The reduction in total pulse length is important, in order to have no significant expansion of the heated matter during the heating phase. For the actual beam parameters this expansion is negligible. During the target heating time, which is equal to the pulse length of the beam (thermalization is several orders of magnitude fas-
Fig. 3. Specific energy deposition along the beam axis in a lead target, width of transversal beam intensity distribution versus penetration depth.
ter), the density of the matter stays constant. The range does not change significantly in comparison to the solid lead target, where the ions have a penetration depth of 11 mm. The spatial distribution of the specific energy deposition is determined by the shape of the beam envelope. The energy loss dE/dx increases with the penetration depth of the ions in the target. To calculate the deposition at the location of the Bragg peak, energy spread, energy loss straggling and angular straggling of the ions have to be taken into account. Fig. 3 shows the calculated longitudinal profile of the deposited energy at the position of the beam axis assuming constant density. In the lower part of the diagram, the beam envelope is plotted. The targets are mounted in a vacuum chamber. Using a high precision vacuum feedthrough, it is possible to adjust each target with respect to the beam axis. Two different geometries are used for the experiments with lead targets. The first configuration is a lead sheet of 1 mm thickness (Fig. 4a). The hydrodynamic motion of the heated target matter can be observed with a fast multiframing camera [4] and an optical backlighter. The direction of observation (x in Fig. 1) is perpendicular to the beam direction (z) and parallel to the surface of the lead sheet. The target is illuminated from the rear side with a xenon flash lamp. The shadow of the expanding matter is recorded with the camera.
I. OVERVIEWS
64
S. Sto( we et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 61—67
The method, called time-resolved shadowgraphy, visualizes the hydrodynamic processes in 60 frames with a minimum interframing time of 1.7 ls. The second configuration consists of a lead cylinder, with implemented piezoelectric pressure gauges (Fig. 4b). The lead cylinder has a diameter of 17 mm, resulting in large volume of not directly heated matter around the interaction zone in comparison to the first target configuration. The gauges
are foils of polyvinylidene flouride (PVDF) with 25 lm thickness [5], having an active area of 5 mm2 and a sensitivity of 25 pC/N. The radial distance of the gauges to the beam axis is between 4 and 6 mm. The pressure wave passing the gauge causes a current signal in the electrical circuit of the gauges, which is recorded with a fast storage oscilloscope. The integrated signal is a measure of the pressure development with time. From the measured propagation time and amplitude, conclusions on the initial pressure conditions of the heated matter at the beam axis can be drawn.
3. Hydrodynamic response of heavy ion heated lead targets
Fig. 4. Lead-target geometry; (a) lead sheet (b) lead cylinder with implemented gauge.
In July 1997 first experiments to investigate the hydrodynamic response of a heavy-ion heated lead target were carried out. The lead sheet target configuration, described in the previous chapter (Fig. 4a), was adjusted in a way, that the focal plane of the plasma lens lies at the position of the Bragg peak inside the lead target. The beam axis coincides with the middle of the lead sheet. Fig. 5 shows six different frames, which show the expansion of the target at different time stages. The exposure time of
Fig. 5. Hydrodynamic expansion of a 1 mm thick lead sheet. s: shadow of solid lead, which was piled up in a previous shot at a different x-position on the sheet
S. Sto( we et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 61—67
65
4. Computer simulations of the hydrodynamic expansion
Fig. 6. Signal of two piezo-electric pressure gauges. The time resolution due to the thickness of the gauge is 10 ns.
each frame is 3.5 ls. The expansion of the lead in transversal direction is symmetric to the beam axis and the velocity of the material remains constant during the observation time of 40 ls. The vertical expansion velocity at the target entrance is 230$20 m/s. The velocity increases with the penetration depth of the ions in the target. At the location of the Bragg peak it reaches a maximum of 290 $20 m/s. The velocity of the matter, which is ejected from the target in longitudinal direction, has the reverse sign of the projectile velocity. The front of the expanding matter propagates with a speed of 210$30 m/s at the beam axis. Using the second target configuration it is possible to measure the shape and amplitude of pressure waves, which propagate from the beam—target interaction zone to outer target regions. Fig. 6 shows the pressure—time development, recorded with two gauges. Gauge 1 has a distance of 6 mm to the beam axis, gauge 2 a distance of 4 mm. The corresponding amplitudes are 0.16 GPa for gauge 1 and 0.10 GPa for gauge 2. The shape of the pressure pulse can be explained by the beam pulse structure, which is represented by the dashed curve (intensity in a.u.) and by the spatial beam intensity profile. No shockwave-like sharp pressure rise can be observed. The maximum of the pressure pulse propagates with 1.9$0.1 km/s through the observed radial region (4—6 mm), which is close to the sound velocity in lead [6].
In collaboration with the Institute of Chemical Physics (ICP) in Chernogolovka numerical simulations are carried out to understand the beam-target interaction and hydrodynamic phenomena. With the simulation it is possible to calculate the specific energy deposition in the target, taking into account the expansion of the matter, i.e. the change in density. The simulations are carried out with a 2-D hydrodynamic code, which treats interfaces with the Godunov method in moving grids [7]. The code uses a semi-empirical wide range equation of state [8]. The beam parameters such as beam envelope, energy and pulse shape are adapted to match the experimental data. The specific energy deposition is computed using the stopping power tables by Biersack and Ziegler [9]. One possible check for the simulation is a comparison with the pressure development in time, as measured with the piezoelectric gauges. The data of the simulation, which correspond to the experimental result in Fig. 6 are plotted in Fig. 7. The calculation is done in the plane, which is perpendicular to the beam axis at a penetration depth of 6 mm. The shape of the positive pressure pulse fits the experimental data well. The pulse amplitudes are 0.34 GPa (gauge 1) and 0.19 GPa (gauge 2) and thus by a factor of two higher than in the experiment. We assume, that this deviation is caused by the implementation of the gauges in a thin layer of
Fig. 7. Simulated pressure—time development at the position of the gauges.
I. OVERVIEWS
66
S. Sto( we et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 61—67
Fig. 8. Energy, density, pressure and temperature distribution after 1200 ns, simulated with a 2-D hydrodynamic code.
Fig. 9. Temperature and density of heavy-ion-induced plasmas at GSI.
epoxy glue. This layer of a matter with lower acoustic impedance than lead is not taken into account in the calculation, which yields only the pressure in an infinite lead cylinder. The reason for the deviation in the arrival time of the pulses is the accuracy in
the experimental determination of the transversal gauge position with respect to the beam. Behind the positive pressure pulse, an expansion wave with negative pressures propagates through the target. This phenomenon, which is caused by the cohesive
S. Sto( we et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 61—67
forces in the dense matter, is not observed in the experiment. There is no explanation up to now, why this negative pulse is not recorded by the pressure gauges. A simulation with the same input parameters is carried out in a plane, which contains the beam axis. Cylindrical symmetry is assumed. Fig. 8. shows energy, pressure, density and temperature distribution in the lead target at a time of 1200 ns, which is 600 ns after the end of the heating phase. The range of the ions during the heating phase is not significantly enlarged by the dilution of the matter in the interaction zone. The maximum temperatures (2800 K) and pressures (3.8 GPa) are reached at t"400 ns in the center of the Bragg peak.
5. Conclusions and outlook The research in heavy-ion induced dense plasmas will benefit from the high intensity upgrade of the GSI accelerator facilities, which will be completed in 1999. The total kinetic beam energy will be in the range of 1 kJ, which is two orders of magnitude higher than the present beam energy. The pulse length of the beam is expected to be lower than 100 ns. This upgrade will lead to a specific energy deposition of more than 100 kJ/g and temperatures
67
between 1 and 10 eV at almost solid-state densities [10], enabling interesting experiments in the regime of non-ideal plasmas. Fig. 9 shows the parameter region, i.e. density and temperature of the target plasma, which are achievable with the present setup and after the upgrade 1999. In addition, the regions of different fusion plasmas are drawn: The sun, a magnetic fusion plasma, a converter plasma in an ICF-facility and the fuel of an ICF-pellet after compression are given as reference points on this “map”. References [1] [2] [3] [4] [5] [6]
[7] [8] [9] [10]
M. Dornik, Fusion Eng. and Des. 32—33 (1996) 511. U.N. Funk, Nucl. Instr. and Meth. A 415 (1998) 68. M. Stetter, Fusion Eng. and Des. 32—33 (1996) 503. Operation Manual of the VFU-1 Camera, ITEP Moscow, 1980 (in Russian). M. Boustie, Laser and Particle Beams 14 (2) (1996) 171. Zelkovich Raiser, Physics of Shockwaves and High-Temperature Hydrodynamic Phenomena II, Academic Press, New York, 1967, 698. V.E. Fortov, Nucl. Sci. and Eng. 123 (1996) 169. A.V. Bushman, Intense Dynamic Loading of Condensed Matter, Taylor & Francis, London, 1992. J.F. Ziegler, The Stopping and Range of Ions in Matter, vol. 1, Pergamon, Oxford, 1985. R.W. Mu¨ller, GSI-Report-96-07, Darmstadt, 1996.
I. OVERVIEWS