A Plan of Warm-Dense-Matter Experiment Using Precompressed Hydrogen Targets

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) 100-300 GPa 0.5 -1 eV Dense hydrogen EOS is important to understand the structure of a giant-gas planet, such as Jupiter.

3. To access off-Hugoniot regimes, a quasi-isentropic pre-compression scheme were proposed. Concept of the beam heating of isentropically pre-compressed target: Hydrogen EOS (SESAME5251) • 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. Target parameter Metal liner Heavy ion bunch Electro-magnetic force

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. Similarity solutions invariant: (Self-similarity coordinate) Reduced fluid equations: Isentropic relation

6. Self-similar solution of uniform compression • Uniform density at rest: • Isentropy: • Cylindrical geometry: M: Mach number before stagnation M=0.4 M=0.5 M=0.6 C=3.6 C=5.6 C=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. Induction cavities Applications Combined function magnet Ion source Machine parameters 200kV H.V. Terminal for 9.4 GHz ECR ion source

11. Numerical simulation on induction acceleration and confinement of Ar18+. by Tanuja Dixit near Injection 20 msec Extraction B(t) 10 Hz operation 0.84 T 5 msec 30 msec Acceleration region t Injection 100 msec 10 msec 40 msec Vac=rC(dB/dt) 15 msec 50 msec

12. Expected beam intensity was evaluated: 109 to 1011 particles per bunch is available depending on projectile Z. Final kinetic energy: Bmax = 0.87 T, R = 3.3 m The space-charge-limited number of ions per bunch: Np = 3x1012, Vi = 200 kV, Vp = 40 MV, (Bf)AIA = 0.7, (Bf)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. Appendix: a concept of beam-induced high pressure field experiments. Beam-driven shock Test material Temperature distribution in depth Beam bunch High-pressure field Beam-heated target Quasi-uniform energy deposition profile

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