Beam–plasma interaction experiments using electromagnetically driven shock waves

ARTICLE IN PRESS Nuclear Instruments and Methods in Physics Research A 606 (2009) 205–211

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Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima

Beam–plasma interaction experiments using electromagnetically driven shock waves J. Hasegawa , H. Ikagawa, S. Nishinomiya, T. Watahiki, Y. Oguri Research Laboratory for Nuclear Reactors, Tokyo Institute of Technology, 2-12-1-N1-14 Ookayama, Meguro-ku, Tokyo 152-8550, Japan

a r t i c l e in fo

abstract

Available online 24 March 2009

Electromagnetically driven shock tubes compatible with in-beam experiments have been developed to examine the stopping power of hot or warm matter over a wide temperature range. The beam–plasma coupling constant g was calculated under various operating conditions of the shock tube. We found that g0.1 is achievable with 10 keV/u Pb ions and a fully ionized plasma produced by a shock wave with 70–80 km/s in a hydrogen gas of 6–9 kPa. The dissociation effect on the hydrogen stopping power for low-energy protons was also evaluated and a 40–50% increase in the stopping cross-section of dissociated hydrogen was predicted in a projectile energy region of 10–40 keV. For the demonstration of the energy loss measurement using shock-heated gas targets, the developed shock tube was embedded into the beam line and tested on its shock-production abilities. In the preliminary experiment using 375 keV/u carbon projectiles, we successfully detected the signal of a carbon ion penetrating a shockheat hydrogen target and observed a decrease in the signal height, which probably corresponds to the energy loss. & 2009 Elsevier B.V. All rights reserved.

Keywords: Stopping power Heavy ion inertial confinement Beam interactions with plasma Shock wave

1. Introduction The precise knowledge of heavy ion stopping in warm or hot matter is essential to predict beam-energy-deposition profiles not only in heavy-ion-fusion targets but also in targets for acceleratordriven warm-dense-matter experiments. In both applications a temperature rise in the target induced by high-power-beam irradiation causes vaporization, dissociation, and ionization of the target material, leading to a change in the stopping power. These temperature effects on the stopping power become more particular for projectiles having a ‘‘Bragg-peak velocity’’, which roughly corresponds to a mean electron velocity in the target. At relatively high target temperatures of more than several electron volts, free electrons in the target causes an enhancement of the stopping power, which is explained by a decrease in the target mean excitation energy and an increase in the projectile mean charge. This so-called ‘‘plasma effect’’ has been examined experimentally by many research groups for the last two decades [1–7]. In these studies high-current discharges or high-power lasers produced ‘‘classical’’ plasma targets. In contrast, some numerical analyses recently showed that strong Coulomb coupling between charged particles could modify the free-electron stopping power of dense plasma [8,9]. There have also been some

 Corresponding author.

E-mail address: [email protected] (J. Hasegawa). 0168-9002/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2009.03.102

experimental activities aiming to measure the stopping power of strong coupling plasmas produced by high-explosive-driven shock waves [10,11]. This strong coupling effect causes a nonlinear dielectric response of the stopping medium to the incident particle charge. It can be scaled by a beam–plasma coupling constant g defined by pffiffiffi 3=2 3Z p Gee g (1) f1 þ ðvp =vth Þ2 g3=2 where Zp and vp are, respectively, the charge and velocity of projectile, vth is the thermal velocity of plasma electrons, and Gee is well-known plasma coupling constant between free electrons. Molecular dynamics simulations indicated that the nonlinear effect becomes remarkable even at g0.1 as a reduction of stopping power [12]. As shown clearly in Eq. (1), g decreases rapidly with increasing projectile velocity, meaning that the nonlinear effect is responsible particularly for low-energy projectiles. On the other hand, temperature effects on bound-electron stopping power are also important for warm targets with temperatures around 0.1–1 eV. The dissociation and ionization of the target change the electronic state distribution of the target atoms, leading to a change in the mean excitation energy, i.e. the stopping power. Even in much lower temperature regime, the vaporization of the target also can affect its stopping power because a large increase in the intermolecular distance also causes a modification in the electronic state distribution. As a typical

ARTICLE IN PRESS J. Hasegawa et al. / Nuclear Instruments and Methods in Physics Research A 606 (2009) 205–211

example of this effect, it is well-known that water and water vapor have different stopping powers from each other [13]. To examine experimentally these temperature effects on the stopping power over a wide temperature range of 0.1–10 eV, we proposed using warm dense plasma targets produced in electromagnetically driven shock tubes. If we choose hydrogen gas as a stopping medium, the Bragg-peak velocity ranges from 100 keV/u to 1 MeV/u for heavy ions. For such relatively low-energy projectiles, the shock-produced plasma is more advantageous than conventional discharge plasmas because it induces no magnetic field that causes an unwanted beam loss. Another important feature of the shock-produced plasma is that plasma parameters such as density and temperature can be easily evaluated by solving mass, momentum, and energy conservation equations under a given shock speed. We have so far examined the basic properties of the shockproduced plasma target by using prototype shock tubes. In the previous experiments we achieved shock speeds over 50 km/s in hydrogen gas of order 100 Pa [14]. Time-resolved spectroscopic measurements revealed that the plasma density and temperature behind the shock front has an appropriate spatial and temporal distribution to be used as a target for interaction experiments [15]. On the other hand, an energy loss measurement system compatible with gas targets has been developed in parallel with shock tube development [16,17]. In this system we adopted a twostage differential pumping to confine the target gas and a silicon semiconductor detector to directly measure the energy of single ions. The principal goal of our study is to experimentally examine the nonlinear Coulomb coupling effects on plasma stopping power. In this paper we numerically investigate expected g values under various beam and target conditions. As the first demonstration of the energy loss measurement using the electromagnetically driven shock tube, we plan to measure the dissociation effect on the stopping power of diatomic molecular gas such as hydrogen and nitrogen. We estimate the dissociation effect on the hydrogen stopping power and reveal the optimum shock conditions to create dissociated gas targets. Then we present the results of shock-heated target production using the newly developed shock tubes designed for in-beam experiments. Also, we report the preliminary result of the energy loss measurement using 375 keV/u carbon projectiles and a dissociated hydrogen target.

2. Numerical analyses 2.1. Estimation of g values under various conditions In Eq. (1) the beam–plasma coupling constant g seems to decrease monotonically with increasing projectile velocity. However, it is not true under actual experimental conditions because both the projectile charge Zp and the plasma coupling constant Gee can change with projectile velocity. The mean value of Zp in the target is determined by a balance between ionization and recombination rates for the projectiles, which are functions of the projectile velocity. Meanwhile, the target density must be limited so that the target thickness is smaller than the projectile range, which leads to the dependency of Gee on projectile velocity. In the following analysis we defined the projectile and the target to be, respectively, lead and hydrogen. The geometrical target thickness was supposed to be 1 mm, which is considered as the minimum value when we use 100 mm orifices for the beam penetration of the target. Then we determined the maximum plasma density from a restriction that the projectile range should be 10 times larger than the target thickness. For the range

0.03 Beam-Plasma Coupling Constant γ

206

10 eV

Pb -> H

0.025 0.02 T = 1 eV

0.015 100 eV

0.01 0.005 0 100

1000

104

105

106

Projectile Energy (eV/u) Fig. 1. Dependence of beam–plasma coupling constant on projectile energy for different target temperatures. Target thickness is assumed to be 1 mm.

calculation we used the SRIM code [18]. We also assumed that a charge state equilibrium was always established in the target and used the Betz formula [19] to evaluate the projectile mean charge at a given velocity. Fig. 1 shows estimated g values as a function of projectile velocity for different target temperatures. With a target temperature of 10 eV, g reaches the peak value of about 0.026 at a projectile velocity of around 20 keV/u. With increasing projectile velocity, g rapidly decreases in accordance with the vp dependency of Eq. (1). Meanwhile, the rapid decrease in the low-energy side of the peak is caused by decreases in both Zp and Gee. Thus, we limited the projectile velocity range to 10–50 keV/u in the following calculation. Next, we evaluated shock-produced hydrogen plasma parameters with shock speeds up to 120 km/s by using Hugoniot curves calculated from the SESAME EOS library [20]. The initial pressure of hydrogen gas in the shock tube was varied from 0.13 to 6.7 kPa. Then we calculated the energy loss of 10–20 keV/u Pb ions in the hydrogen plasmas by using an ion stopping calculation code including charge exchange processes of projectiles [7]. The initial projectile charge was varied from 2 to 10. Since g changes with projectile charge and velocity, we averaged it over the ion trajectory in the target. The calculated g for 10 keV/u Pbn+ (n ¼ 2, 4, 6, 8, 10) ions in hydrogen plasmas are plotted as a function of the shock speed in Fig. 2. For every initial charge state of projectile, g has a maximum at a shock speed of 70–80 km/s. The dependency of g on the initial projectile charge becomes more remarkable at shock speeds more than 60 km/s because the recombination of the projectile in the target is strongly suppressed by a significant drop in the bound-electron density accompanying the target ionization. It is obvious from the figure that higher initial projectile charge brings a higher g value. Finally, we summarized the peak g values calculated for different initial gas pressures in Fig. 3. Here, the projectile was also 10 keV Pb ions with an initial charge of 2–10. g increases with increasing initial gas pressure because more dense plasma can be produced under the fixed shock speed. However, higher plasma density leads to too much energy loss of projectiles, which will degrade the accuracy of the stopping power measurement because of a large energy straggling and uncertainty in the projectile velocity in the target. The dashed line in the figure stands for the boundary of DE/E ¼ 50% and the dot-dashed line corresponds to DE/E ¼ 20%, where E is the initial projectile energy. If we allow DE/E ¼ 50%, we can obtain g ¼ 0.08–0.09 for an initial gas pressure of 6–9 kPa. By using higher initial projectile charge,

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excitation energy is written in the local plasma approximation as follows: Z rðrÞ lnð_op ðrÞÞ dV (2) Z 2 ln I ¼

Beam-Plasma Coupling Constant γ

0.08 10-keV/u Pbn+ -> H plasma (1.3 kPa, 1mm)

0.07

2+

0.06

207

4+

where Z2 is the atomic number of the target atom, r(r) is the electron density, and op is the plasma frequency defined by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (3) op ðrÞ ¼ rðrÞe2 =me 0 .

6+

0.05

8+

0.04

10+

0.03 0.02 0.01 0 0

20

40 60 80 Shock Speed (km/s)

100

120

Fig. 2. Dependence of beam–plasma coupling constant on shock speed for different initial projectile charges. The initial projectile energy is fixed to be 10 keV/u.

Here, e and me are, respectively, the charge and mass of an electron, and e0 is the dielectric constant for vacuum. The electron density r(r) was determined from the wave function c as r(r) ¼ |c|2. The wave function of a hydrogen atom in the ground state cH is expressed by using the Bohr radius a0 as  3=2   1 1 r . (4) cH ðrÞ ¼ pffiffiffiffi exp  a0 p a0 For a hydrogen molecule we used a valance bond method and obtained its wave function cH2 as follows [22]:

cH2 ðr1 ; r2 Þ ¼ Afca ðr1 Þcb ðr 2 Þ þ ca ðr2 Þcb ðr1 Þg 

 r a0   r . cb ¼ ð0:07  0:175zb Þ exp 1:19 a0

ca ¼ ð0:07 þ 0:175za Þ exp 1:19

Beam-Plasma Coupling Constant γ

0.14 10-keV/u Pbn+ -> H plasma (1 mm)

0.12 10+ 8+

0.1

ΔE/E = 50%

0.08 0.06

6+ 2+

0.04

4+

0.02 ΔE/E = 20%

0 0

2

4 6 8 Initial Gas Pressure (kPa)

10

12

Fig. 3. Peak values of beam–plasma coupling constant plotted as a function of initial gas pressure of shock tube. The projectile is 10 keV/u Pb with an initial projectile charge from 2 to 10. Dashed-dotted line and dashed line express an energy loss ratio of 20% and 50%, respectively.

we can decrease the initial pressure. In case of DE/E ¼ 20%, the expected g ranges around 0.04. In Fig. 3 only peak values of g corresponding to 70–80 km/s shock speeds are plotted. Even with much lower shock speeds, we could achieve g around 0.01–0.03 as shown in Fig. 2. However, the effect of bound electrons on the stopping power does not become negligible, which may make the analysis of the experimental results more complex.

2.2. Stopping power calculation for dissociated hydrogen target In the experiments with shock-produced dissociated gas targets, we plan to use hydrogen or nitrogen as a driven gas. Here we evaluate the dissociation effect on the stopping power of hydrogen gas for low-energy protons. To evaluate the mean excitation energy of hydrogen atom and molecule, we used a local plasma approximation [21]. This approximation treats atomic electrons as a free electron gas confined in an attractive potential induced by nuclear charge, which gives distributions of atomic potential and electron density in a reasonable accuracy. The mean

(5)

In the above equations, suffixes a and b are used to distinguish two hydrogen nuclei and suffixes 1 and 2 are for two electrons. z is the distance of the nucleus center from the centroid of the hydrogen molecule. By using Eqs. (2)–(5), we calculated the mean excitation energy of a hydrogen atom and a hydrogen molecule to be 12.1 and 19.1 eV, respectively. The calculated mean excitation energy of a hydrogen molecule was in good agreement with the experimental value (19.2 eV) determined from the measured stopping power [23]. Thus, we concluded that our calculation using the local plasma approximation was reliable. A large decrease in the mean excitation energy for hydrogen accompanying its dissociation is attributed to a decrease in the binding energy of bound electrons. Since neither the LSS formula nor the Bethe–Bloch formula, which are commonly used for stopping power calculations, considers the effect of bound-electron velocity, they are not applicable to the stopping power calculation around the Braggpeak velocity. Then, we used a stopping power formula based on a classical collision theory for two moving charged particles derived by Ku¨hrt and Wedell [24]: S¼

Z 21 Z 2 e4 8p20 me v21    2me v21 4 4 if Ip2me v1 ðv1  ve Þ  þ ln I 3 (  pffiffiffi  v1 4v 1 2þ 22   1 þ  pffiffiffi ve 3v 3 2þ1  2ðv1 =ve þ 1Þ if 2me v1 ðv1  ve ÞpIo2me v1 ðv1 þ ve Þ þ ln pffiffiffi 2þ1  0 in all other cases.

(6)

Here, the bound electron velocity ve was calculated from the pffiffiffiffiffiffiffiffiffiffiffiffiffi mean excitation energy as ve ¼ 2I=me . Stopping cross-sections calculated for hydrogen atom and molecule are plotted and compared in Fig. 4. We see that the dissociation of hydrogen causes a 20% increase in the peak stopping cross-section and a peak energy shift of about 10 keV towards the low-energy side. In the energy range from 10 to 40 keV, the enhancement of the stopping power reaches around 50%, which will be actually detectable in the experiment.

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10

7

Hydrogen atom

6 5 4 3

Hydrogen molecule

Number Density (1023 m-3)

Stopping Cross Section (10-15eV cm2)

8 H2 p0 = 100 Pa T0 = 300 K

1

H

H2 e–

0.1 0

2

10

20 30 Shock Speed (km/s)

40

50

1 100 Proton Energy (keV) Fig. 4. Stopping cross-sections for hydrogen molecule and hydrogen atom calculated for low-energy protons.

2.3. Evaluation of optimum shock speeds for dissociated gas targets The accuracy of Hugoniot depends strongly on the accuracy of the EOS used. We have been using the SESAME library for hydrogen in the above evaluation of g values. On the other hand, some of the SESAME data tables for diatomic molecule gas such as nitrogen and oxygen are inaccurate at a temperature range above 1 eV because they cannot treat the dissociation of molecules in a proper way. Thus, we developed an original EOS code (IGEOS) for ideal gas composed from diatomic molecules, which can solve dissociation and ionization equilibriums self-consistently. In a relatively low temperature regime below 5000 K, the code calculates vibrational energy as a function of temperature, but treats rotational energy as a constant value because the rotational degrees of freedom are excited in a molecular gas at very low temperatures around the order of 10 K [25]. On the other hand, we neglected Coulomb interactions between the charged particles because they just give small corrections to the EOS at very high temperatures more than 105 K. We confirmed that the IGEOS well reproduced the SESAME EOS for hydrogen. So, we adopted the IGEOS for the following Hugoniot calculations for dissociated gas targets. Fig. 5 shows the calculated number densities of molecules, atoms, and free electrons as a function of shock speed in a shockheated hydrogen and nitrogen with an initial pressure of 100 Pa and an initial temperature of 300 K. The number density of the neutral hydrogen atom has a peak with a shock speed around 25 km/s and a dissociation degree of 98%. We can get higher dissociation degrees more than 99% by increasing the shock speed. However, an increase in the free electron density may disturb the observation of the dissociation effects on the stopping power. Thus, here we defined the optimum shock speed for dissociated hydrogen gas target to be 24 km/s. The optimum shock speeds were almost independent of the initial gas pressure.

3. Experimental setup Fig. 6 illustrates electromagnetically driven shock tubes developed for the present study. We used two types of shock tubes having square cross-sections of (a) 5  5 mm2 and (b) 15  15 mm2. The thin shock tube (5  5 mm2) was designed for the generation of non-ideal dense plasma targets, which usually needs a shock speed more than 50 km/s when using hydrogen as a driven gas. This shock tube adopted coaxial discharge electrodes

10 Number Density (1023 m-3)

10

N2 p0 = 100 Pa T0 = 300 K

1

N

e–

N2

0.1 0

5

10 Shock Speed (km/s)

15

20

Fig. 5. Number density of molecules, atoms, and electrons in shock-heated hydrogen and nitrogen as a function of shock speed. Initial pressure and temperature are 100 Pa and 300 K, respectively, for both cases.

to reduce circuit inductance. The angle of the tapered section (301) was carefully optimized to obtain as high a shock speed as possible [26]. The position of the beam injection was 35 mm from the bottom end of the tube. On the other hand, the thick tube (15  15 mm2) was used to produce fully dissociated gas targets. To ensure the formation of strong shock waves, the shock propagation distance (77 mm) was designed to be much larger than that in the thin tube. This tube adopted parallel planer electrodes for discharge. In the driving circuit for the thin tube, we used a capacitor bank of 1.8 mF composed from low-inductance-type capacitors to get as short a current rise time as possible. In contrast, the thick tube was driven by a 4.4 mF capacitor because the discharge current period should be long enough to keep a driving force during shock propagation. The operating principle of the shock tube is as follows. After the spark gap switch was turned on, a discharge current up to several tens of kilo-amperes produced a discharge plasma at the bottom end of the tube. An electromagnetic force between the current flowing in the plasma and the return current accelerated this ‘‘piston’’ plasma toward the top end of the tube. The strong shock formed in front of the piston plasma compressed and heated a gas, which was filled in the tube beforehand. Finally, we obtained a hot and dense gas (or plasma) target just behind the shock wave. To suppress the unwanted noise from the discharge circuit, the capacitor and the spark gap switch were placed in a copper shielding cage and the discharge current was supplied to the shock tube electrodes via four coaxial cables. A Rogowski coil was used to monitor the discharge current waveform to know the exact time of the discharge initiation. The shock tube was filled by hydrogen gas with a pressure of 0.1–1 kPa before the operation. We could not use thin foils as beam injection window because the beam energy loss in the foil

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209

Fig. 6. Two types of shock tubes developed for the production of (a) non-ideal plasma targets and (b) fully dissociated gas targets.

(

( Fig. 7. Experimental setup for energy loss measurement using a shock-produced target.

was comparable to or larger than that in the target in the present experimental conditions. Thus, to sustain the large pressure difference between the shock tube and the beam line, we adopted a two-stage differential pumping system as shown in Fig. 7 [16]. In the first stage of the differential pumping, a couple of 100-mmdiameter apertures on the tube wall sustained a pressure difference of order kPa between the shock tube and the intermediate chamber. A turbo molecular pump evacuated the gas flowing out through those apertures and kept the intermediate chamber at a pressure of several orders of Pa. On the other hand, the second apertures located at both ends of the intermediate chamber (3 mm in diameter and 10 mm in thickness) kept the pressure of the beam line below 103 Pa. A piezo actuator valve precisely controlled the gas flow rate into the tube to obtain a required initial gas pressure. After every discharge the gas in the tube was flushed by a vacuum pump connected directly to the gas feeding line. Because of very low ion transmission through the 100-mmdiameter apertures on the tube wall, it is very difficult to apply the conventional TOF method to the energy loss measurement in the present study. Thus, we used a beam energy measurement system based on a fast beam kicker and a silicon semiconductor detector [16]. In this system the kicker clipped a pulsed beam of 200 ns

duration from a dc beam supplied by an electrostatic accelerator. The timing between the pulsed beam injection into the shock tube and the shock arrival at the beam injection point was carefully adjusted to ensure the interaction between the incident ions and the shock-heated gas (plasma) target. The silicon surface barrier detector (SSBD) at about 2 m downstream of the shock tube directly measured the energy of the single ion passing the shock tube through the 100 mm apertures. A digital oscilloscope directly recorded the output signal from a linear pulse-shaping amplifier connected to the SSBD via a fast preamplifier. The ion transmission through the shock tube further decreased when the beam was injected into the shock-heated gas target because of the increasing scattering probability for the incident ions. We determined the beam current to be about 0.1 nA so that the pulsed beam contained several hundreds of ions to compensate the beam loss in the tube. We need to repeat the energy loss measurement for a single ion many times under the same projectile and target conditions to increase the statistical accuracy of the measured value. Thus, the reproducibility of the shock-heated target is essential. As described before, the quantities of state behind the shock wave can be easily deduced from the shock speed. Relying on this useful feature of the shock wave, we checked the reproducibility of the

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target in every energy loss measurement by monitoring the shock speed with a fast streak camera.

4. Results and discussion The evaluation of the target properties based on the shock speed is valid only when the shock wave is regarded as a onedimensional quasi-steady flow. Thus, we examined the shape of the shock front and the uniformity of the shock-heated gas by a fast streak camera. Fig. 8 shows a typical streak image of the shock-heated gas target produced by the thick shock tube (Fig. 6b). In this observation the slit of the streak camera was placed at the same height as the beam line and set to be perpendicular to the shock flow direction. A planar shock over the whole width of the shock tube was observed as shown in the figure, indicating that a one-dimensional strong shock wave was successfully formed at the beam injection point. The emission

45

45

40

40

35

35 Shock speed (km/s)

Shock Speed (km/s)

Fig. 8. A typical streak image of shock-heated hydrogen gas in a 15  15 mm2 shock tube.

from the shock-heated gas is almost uniform just after the shock front, but its uniformity degrades with increasing distance from the shock front. This degradation limits its lifetime as a target for interaction experiments. When using the thin shock tube (Fig. 6a), we also successfully obtained planner shock waves. However, the target lifetime seemed to be shorter than the above result, which may be attributed to the difference in the discharge current period. To evaluate shock speed we recorded the motion of the shock front by placing the streak camera slit to be parallel to the flow direction. From the slope of the shock front trace in the streak image, we determined the shock speed at the beam injection point. In Fig. 9 we plotted the measured shock speed as a function of charging voltage for both types of shock tubes. Each data point in the figure shows a shock speed averaged over 10 different shots and the error bar expresses its standard deviation. In both cases the shock speed increases proportionally to the charging voltage. We achieved a shock speed of about 40 km/s in the thin shock tube with a charging voltage of 15 kV, which is larger than the shock speed obtained with a prototype shock tube at the same charging voltage in the previous experiments [14]. On the other hand, the thick shock tube also achieved a shock speed of 25 km/s in a 1.2 kPa hydrogen gas, which meets the requirement defined by the numerical analysis given in Fig. 5a. Even at the same discharge voltage, the shock speed varied from shot to shot with a variation of around 20%. This is probably due to the poor reproducibility of the piston plasma generation at the bottom end of the tube. The use of hemispherical electrodes as in the spark gap switch will stabilize the spark and solve this problem. Fig. 10 compares typical output waveforms from the linear proportional amplifier with and without the shock-heated gas target. Thanks to the careful shielding of the pulse power circuit, the duration of the discharge noise drastically decreased to less than 3 ms. Then we could successfully separate the beam signal from the noise by using a time interval between the discharge initiation and the shock arrival although the amplitude of the noise was still harmful. We observed a decrease in signal height, which was probably caused by the energy loss of the carbon ion in

30

25

30

25

20

20

15

15

5x5 mm2 H2 : 3.0 kPa

15x15 mm2 H2 : 1.2 kPa

10

10 9

10

11 12 13 14 15 Charging Voltage (kV)

16

14

15 16 17 Charging Voltage (kV)

18

Fig. 9. Measured shock speeds as a function of charging voltage with (a) 5  5 mm2 shock tube and (b) 15  15 mm2 shock tube.

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Discharge

Linear Amplifier Output (V)

2

hydrogen plasma. The optimal shock velocity determined by the Hugoniot calculation was achieved actually by using the newly developed shock tube. In this preliminary interaction experiment, we succeeded in observing the signal of a carbon ion penetrating the shock-heated gas target. A decrease in the signal height was also observed, but much more number of data must be gathered to increase the statistical accuracy of the measured energy loss value and compare it with the theoretical prediction.

w/o target

Noise

ΔE

211

w/ target

1

0 Beam Signals

Acknowledgement

-1 0

2

4

6 Time (μs)

8

10

12

Fig. 10. Typical output signals from a linear pulse-shaping amplifier with and without the shock-heated hydrogen target.

the shock-heated gas target. However, we should accumulate much more data to make the result statistically meaningful. According to the discharge waveforms observed by the Rogowski coil, the switching jitter was less than 10 ns, which was small enough to synchronize the target plasma generation and the beam injection. However, the large variation in the shock speed caused a jitter of several hundred nanoseconds in the shock arrival time at the beam injection point, which largely reduced the data collection efficiency. To obtain better statistics in the energy loss measurement, the increase in the reproducibility of the shock speed is the primary issue. Moreover, the shock speed measurement relying on the streak image should be reviewed because the edge of the shock trace on the image was not so sharp because of the relaxation layer just after the shock front, which also brings a measurement error to the shock speed. 5. Concluding remarks A numerical model evaluated the beam–plasma coupling constant g under various experimental conditions and found that g0.1 is achievable with 10 keV/u Pb ions and a fully ionized plasma produced by a strong shock wave with 70–80 km/s in a hydrogen gas of 6–9 kPa if a 50% energy loss is acceptable. By decreasing the initial gas pressure, we can increase the measurement accuracy because of lower energy loss ratios (p20%), but g is limited to be around 0.02–0.04. The stopping power calculation based on a classical collision theory showed that in the energy region below the Bragg peak, the stopping cross-section of hydrogen atom is about 40–50% larger than that of hydrogen molecule because of the large difference in their mean excitation energies. We consider that this difference is actually detectable in the measurement. As the first demonstration of the energy loss measurement using the shock-heated gas target, we performed the measurement of the energy loss of 375 keV/u carbon in a dissociated

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