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Two-dimensional simulations of KALIF beam–target interactions
Nuclear Instruments and Methods in Physics Research A 415 (1998) 677—679
Two-dimensional simulations of KALIF beam—target interactions H. Marten!,*, K. Baumann!, B. Goel!, A.V. Shutov" ! Forschungszentrum Karlsruhe GmbH, Inst. f. Neutronenphysik and Reaktor. Postfach 3640, 76021 Karlsruhe, Germany " ICP Chernogolovka, 142432 Moscow region, Russia
Abstract Beam—target interaction experiments performed at the Karlsruhe Light Ion Facility (KALIF) have previously been simulated by one-dimensional (1D) radiation hydrodynamics in slab geometry, which implies a spacially homogeneous beam power distribution. In this paper the consequences of a non-homogeneous beam power distribution are studied by 2D hydrodynamical simulations. It is shown that — for conditions valid at KALIF — time and space resolved measurements of the target back surface velocity can be used to deduce information on the spacial beam profile. ( 1998 Elsevier Science B.V. All rights reserved.
In foil acceleration experiments performed with the high-voltage pulsed power generator KALIF, Aluminum foils with initial thicknesses of several tens of micrometers are ablatively accelerated by intense proton beams, and foil velocities larger than 10 km/s have been measured with a space and time resolving laser-Doppler velocimeter [1]. We present two-dimensional hydrodynamic simulations of these experiments using a Godunov-type scheme on moving grids in cylindrical symmetry [2]. The equation of state (EOS) used in these computations is the multi-phase wide-range EOS of Aluminum given in Ref. [3]. The stopping power of the protons (energy loss per unit length) is computed by the semiempirical formulae of Ref. [4], which describe the enhancement of the stopping power as a function of heating and its decrease with the expansion
* Corresponding author.
of matter. The results of these formulae are comparable to a more detailed model described previously and used to interpret energy deposition experiments at KALIF [5]. In this numerical study Aluminum foils of 33 and 75 lm initial t hickness are irradiated by protons with parameters following the measured time history of the KALIF B -beam. These protons have # a maximum energy of 1.35 MeV and are focused to a peak power density of 0.15 TW/cm2 at the target (see Ref. [6] for more details on the B -beam). The # beam power distribution P(r, t) on the target is assumed to be either homogeneous, i.e. P(r, t)" P (t), or Gaussian shaped, i.e. P(r, t)"P (t) 0 0 exp(!r2/2p2), where P (t) is the KALIF power 0 density in the beam center at time t, r is the radial distance from the beam center and p is the standard deviation for the experimentally determined fullwidth at half-maximum of 8 mm. The simulated targets always have a diameter of 1 cm.
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 4 4 7 - 1
678
H. Marten et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 677—679
Fig. 1. Computed density distribution at 18 ns after beam impact on a 33 lm thick Aluminum foil. The densities range from about 7]10~5 (light gray) up to 2.91 g/cm~3 (black). The Gaussian beam comes from the right.
Fig. 1 shows the computed density distribution at t"18 ns after the impact of a Gaussian beam on 33 lm thick Al. The computations start with initial solid density of Al (2.7 g/cm3) between 04z40.0033 cm in Fig. 1. Since the range of the incoming protons is smaller than the initial foil thickness, only a part of the foil is evaporated and expands at temperatures of a few tens of eV to the right of Fig. 1. The corresponding ablation pressure of the expanding plasma compresses the remaining solid part and accelerates it to the left. This solid flyer is seen as a high-density region on the left of the computational domain — curved due to the non-homogeneous power density distribution. The computed back surface velocities of the flyer as a function of the radial position and time are shown in Fig. 2. They show small oscillations with time due to wave reverberations inside the solid part, which are induced by the first strong pressure pulse: the first pressure pulse creates a shock wave which is periodically reflected
between the targets back surface and the plasma— solid interface. Fig. 3 compares the computed back surface velocities as measured in the beam center for homogeneous and Gaussian beam profiles and initial target thicknesses of 33 and 75 lm. The wave reverberations in the 33 lm target are noticed as small oscillations while in the 75 lm target the first shock reflection at the back surface generates a large velocity jump at about 10 ns. Interestingly, the velocities in the centers of homogeneous and Gaussian shaped beams agree quite well, indicating that pressure gradients tangential to the target surface can only be of minor importance for the target dynamics during the first few tens of nanoseconds. Quantitatively, this can be proven by comparing the spacial velocity distribution with the initial Gaussian of the power density. For example, the ratio of power densities from a 2D Gaussian at r"0 and r"p is 0.606. After 20 ns the ratios of the computed back surface velocities at these radii are
H. Marten et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 677—679
679
Fig. 3. Computed back surface velocities in the beam center for spacially homogeneous and for Gaussian beam profiles for two different targets.
sequel of 1D simulations at different radial beam positions without a significant loss of accuracy. Fig. 2. Computed back surface velocity as a function of radial position and time for a Gaussian beam profile. The target is a 33 lm Al foil.
References
+0.59 for 33 lm and +0.67 for 75 lm Al. Due to the large ratio of target diameter to target thickness (here of the order of 100—300) and due to the short measuring period (typically a few tens of nanoseconds in the experiments) radial disturbances do not evolve significantly. Our conclusions are twofold: (1) time and space resolved velocity measurements as done routinely at KALIF can be used to deduce information about the beam profile, and (2) the target dynamics can be studied by a
[1] K. Baumung et al., Laser and Particle Beams 14 (1996) 181. [2] V.E. Fortov, B. Goel, C.-D. Munz, A.L. Ni, A.V. Shutov, O.Yu. Vorobiev, Nucl. Sci. Eng. 123 (1996) 169. [3] I.V. Lomonosov, V.E. Fortov, K.V. Khishchenko, P.R. Levashov, Nucl. Instr. and Meth. A 415 (1998) 604. [4] A.Ya. Polishchuk, V.E. Fortov, V.S. Khloponin, Sov. J. Plasma Phys. 17 (1991) 523. [5] B. Goel, H. Bluhm, J. de Physique 49 Colloque C7 (1988) C7-169. [6] P. Hoppe´ et al., in: Report FZKA 5590, Forschungszentrum Karlsruhe, 1995, p. 51.
Two-dimensional simulations of KALIF beam—target interactions H. Marten!,*, K. Baumann!, B. Goel!, A.V. Shutov" ! Forschungszentrum Karlsruhe GmbH, Inst. f. Neutronenphysik and Reaktor. Postfach 3640, 76021 Karlsruhe, Germany " ICP Chernogolovka, 142432 Moscow region, Russia
Abstract Beam—target interaction experiments performed at the Karlsruhe Light Ion Facility (KALIF) have previously been simulated by one-dimensional (1D) radiation hydrodynamics in slab geometry, which implies a spacially homogeneous beam power distribution. In this paper the consequences of a non-homogeneous beam power distribution are studied by 2D hydrodynamical simulations. It is shown that — for conditions valid at KALIF — time and space resolved measurements of the target back surface velocity can be used to deduce information on the spacial beam profile. ( 1998 Elsevier Science B.V. All rights reserved.
In foil acceleration experiments performed with the high-voltage pulsed power generator KALIF, Aluminum foils with initial thicknesses of several tens of micrometers are ablatively accelerated by intense proton beams, and foil velocities larger than 10 km/s have been measured with a space and time resolving laser-Doppler velocimeter [1]. We present two-dimensional hydrodynamic simulations of these experiments using a Godunov-type scheme on moving grids in cylindrical symmetry [2]. The equation of state (EOS) used in these computations is the multi-phase wide-range EOS of Aluminum given in Ref. [3]. The stopping power of the protons (energy loss per unit length) is computed by the semiempirical formulae of Ref. [4], which describe the enhancement of the stopping power as a function of heating and its decrease with the expansion
* Corresponding author.
of matter. The results of these formulae are comparable to a more detailed model described previously and used to interpret energy deposition experiments at KALIF [5]. In this numerical study Aluminum foils of 33 and 75 lm initial t hickness are irradiated by protons with parameters following the measured time history of the KALIF B -beam. These protons have # a maximum energy of 1.35 MeV and are focused to a peak power density of 0.15 TW/cm2 at the target (see Ref. [6] for more details on the B -beam). The # beam power distribution P(r, t) on the target is assumed to be either homogeneous, i.e. P(r, t)" P (t), or Gaussian shaped, i.e. P(r, t)"P (t) 0 0 exp(!r2/2p2), where P (t) is the KALIF power 0 density in the beam center at time t, r is the radial distance from the beam center and p is the standard deviation for the experimentally determined fullwidth at half-maximum of 8 mm. The simulated targets always have a diameter of 1 cm.
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 4 4 7 - 1
678
H. Marten et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 677—679
Fig. 1. Computed density distribution at 18 ns after beam impact on a 33 lm thick Aluminum foil. The densities range from about 7]10~5 (light gray) up to 2.91 g/cm~3 (black). The Gaussian beam comes from the right.
Fig. 1 shows the computed density distribution at t"18 ns after the impact of a Gaussian beam on 33 lm thick Al. The computations start with initial solid density of Al (2.7 g/cm3) between 04z40.0033 cm in Fig. 1. Since the range of the incoming protons is smaller than the initial foil thickness, only a part of the foil is evaporated and expands at temperatures of a few tens of eV to the right of Fig. 1. The corresponding ablation pressure of the expanding plasma compresses the remaining solid part and accelerates it to the left. This solid flyer is seen as a high-density region on the left of the computational domain — curved due to the non-homogeneous power density distribution. The computed back surface velocities of the flyer as a function of the radial position and time are shown in Fig. 2. They show small oscillations with time due to wave reverberations inside the solid part, which are induced by the first strong pressure pulse: the first pressure pulse creates a shock wave which is periodically reflected
between the targets back surface and the plasma— solid interface. Fig. 3 compares the computed back surface velocities as measured in the beam center for homogeneous and Gaussian beam profiles and initial target thicknesses of 33 and 75 lm. The wave reverberations in the 33 lm target are noticed as small oscillations while in the 75 lm target the first shock reflection at the back surface generates a large velocity jump at about 10 ns. Interestingly, the velocities in the centers of homogeneous and Gaussian shaped beams agree quite well, indicating that pressure gradients tangential to the target surface can only be of minor importance for the target dynamics during the first few tens of nanoseconds. Quantitatively, this can be proven by comparing the spacial velocity distribution with the initial Gaussian of the power density. For example, the ratio of power densities from a 2D Gaussian at r"0 and r"p is 0.606. After 20 ns the ratios of the computed back surface velocities at these radii are
H. Marten et al. /Nucl. Instr. and Meth. in Phys. Res. A 415 (1998) 677—679
679
Fig. 3. Computed back surface velocities in the beam center for spacially homogeneous and for Gaussian beam profiles for two different targets.
sequel of 1D simulations at different radial beam positions without a significant loss of accuracy. Fig. 2. Computed back surface velocity as a function of radial position and time for a Gaussian beam profile. The target is a 33 lm Al foil.
References
+0.59 for 33 lm and +0.67 for 75 lm Al. Due to the large ratio of target diameter to target thickness (here of the order of 100—300) and due to the short measuring period (typically a few tens of nanoseconds in the experiments) radial disturbances do not evolve significantly. Our conclusions are twofold: (1) time and space resolved velocity measurements as done routinely at KALIF can be used to deduce information about the beam profile, and (2) the target dynamics can be studied by a
[1] K. Baumung et al., Laser and Particle Beams 14 (1996) 181. [2] V.E. Fortov, B. Goel, C.-D. Munz, A.L. Ni, A.V. Shutov, O.Yu. Vorobiev, Nucl. Sci. Eng. 123 (1996) 169. [3] I.V. Lomonosov, V.E. Fortov, K.V. Khishchenko, P.R. Levashov, Nucl. Instr. and Meth. A 415 (1998) 604. [4] A.Ya. Polishchuk, V.E. Fortov, V.S. Khloponin, Sov. J. Plasma Phys. 17 (1991) 523. [5] B. Goel, H. Bluhm, J. de Physique 49 Colloque C7 (1988) C7-169. [6] P. Hoppe´ et al., in: Report FZKA 5590, Forschungszentrum Karlsruhe, 1995, p. 51.