1. A Plan of Warm-Dense-Matter Experiment Using Precompressed Hydrogen Targets J. Hasegawa, Y. Oguri, and K. Horioka (Tokyo Tech) K. Kikuchi and T. Sasaki (Nagaoka Univ. of Tech.) S. Kawata (Utsunomiya Univ.) K. Takayama (KEK)

2. A warm dense matter experiment is planned using intense heavy-ion bunches from KEK Digital Accelerator. KEK Digital Accelerator (KEK-DA): –A heavy ion super bunch is accelerated and confined by induction voltages. –A wide range of ion species, even clusters, can be accelerated. –The super bunch supplies a specific energy deposition of kJ/g on target. A WDM experiment is planned as one of the applications of KEK-DA. –The high-energy beam from KEK- DA allows uniform bulk target heating and well-defined energy deposition. –Measurement of hydrogen equation of state under ~200 GPa, ~6000 K requires not only heating but also compression of the hydrogen target. KEK Digital Accelerator (former KEK-booster) Dense hydrogen EOS is important to understand the structure of a giant- gas planet, such as Jupiter. 100-300 GPa 0.5 -1 eV

3. To access off-Hugoniot regimes, a quasi-isentropic pre- compression scheme were proposed. Advantages: –The tailored driving force allows shock-free, quasi-isentropic compression. –Instantaneous bulk heating by an intense beam bunch achieves well- defined uniform energy deposition. –The large aspect ratio of the cylindrical target guarantees one-dimensional treatment. Metal liner Electro- magnetic force Concept of the beam heating of isentropically pre-compressed target: Heavy ion bunch Hydrogen EOS (SESAME5251) Target parameter

4. The isentrope almost coincides with the cold curve (isotherm at T=0). Pressure of a solid: Grüneisen coefficient for solid hydrogen was evaluated from SESAME cold curve data. An isentropic relation between the pressure and volume: : Grüneisen coefficient

5. Equations for scale-invariant similarity solutions were solved. Reduced fluid equations: Similarity solutions invariant: (Self-similarity coordinate) Isentropic relation

6. Self-similar solution of uniform compression Uniform density at rest: Isentropy: Cylindrical geometry: M=0.4M=0.5M=0.6 M: Mach number before stagnation C=3.6C=5.6C=10

7. Driving current waveform required for isentropic compression was determined from the trajectory of outermost fluid particle. Mechanical power acting on solid hydrogen surface: Magnetic pressure induced by current: Required driving current: After rising gradually, the driving current increases more rapidly particularly for higher compression ratios. A power supply based on pulse forming network is suitable for pulse tailoring.

8. A typical example of isentropic compression and driving current waveform. Target conditions: –Final target radius = 1 mm –Compression ratio = 5.6 Normalization factors: –Initial target radius: –Imploding time: A peak current of ~400-500 kA and a rise time of 1.5 µs is required to implode the target. : Sound velocity

9. Required peak current and total energy of the driving circuit was estimated for various target sizes and compression ratios. Restricting conditions: –Target radius after compression is defined by the beam radius on target achievable in the final beam focusing system. (0.1 mm ~10 mm) –Compression factor is determined by required final pressure. (1.8 ~ 10) –Final beam radius less than 1 mm is realistic; larger target requires MA driving current and MJ energy.

10. The KEK booster-PS is now being reconstructed as KEK Digital Accelerator by installing induction cavities. Applications Induction cavities Combined function magnet Ion source 200kV H.V. Terminal for 9.4 GHz ECR ion source Machine parameters Bending radius3.3 m Ring circumference37.7 m Maximum flux density1.1 T Accele. voltage/turn3.24 kV Repition rate10 Hz Betatron tune x / y 2.1/2.3

11. near Injection 5 msec 10 msec 15 msec 20 msec 30 msec 40 msec 50 msec 10 Hz operation Numerical simulation on induction acceleration and confinement of Ar 18+. by Tanuja Dixit t B(t) Acceleration region Injection Extraction V ac =  C(dB/dt ) 100 msec 0.84 T

12. Expected beam intensity was evaluated: 10 9 to 10 11 particles per bunch is available depending on projectile Z. Final kinetic energy: The space-charge-limited number of ions per bunch: B max = 0.87 T,  = 3.3 m N p =  , V i = 200 kV, V p = 40 MV, (B f ) AIA = 0.7, (B f ) RF = 0.3

13. A specific energy deposition more than 100 kJ/g is available with a beam spot radius less than 0.2 mm. Specific energy deposition was estimated from SRIM stopping data. The heavier projectile can supply higher specific energy deposition. The minimum requirement for the specific energy deposition is about 100 kJ/g. A beam spot radius less than 0.2 mm is preferable.

14. Summary An accelerator-driven WDM experiment using a quasi-isentropically compressed target was proposed to investigate material properties in the off-Hugoniot regime. Scale-invariant self similar analysis was used to evaluate required experimental conditions, such as target size, driving power, and current waveforms. A final target radius after compression should be less than 1 mm to design actually adoptable power supplies. To examine the feasibility of this scheme more in detail, MHD simulations coupled with the external driving circuit will be performed. Beam energy deposition by a heavy ion beam bunch from KEK-DA was also estimated. A specific energy deposition more than 100kJ/g will be available, which is enough to reach the required WDM conditions.

15. MethodsMax. pressureFeatures Diamond anvil~ 60 GPaStatic, easy control, easy measurement Laser-driven shock wave~ TPaDynamic, extremely high pressure, compact equipment Beam-driven shock wave~100 GPa?Dynamic, well-defined shocks, bulk heating, Controllable temporal evolution. Appendix: a concept of beam-induced high pressure field experiments. Temperature distribution in depth Quasi-uniform energy deposition profile Beam bunch Beam-driven shockTest material High-pressure field Beam-heated target

16. Appendix: an extremely high pressure field is induced in the material by intense beam irradiation. With Pb tamper Without Pb tamper Controllable pressure history Pressure in Al 1D hydro code (with radiation transport):