Semi-empirical Studies of Warm-Dense-Matter Physics using Fast Pulse Power Device

Transcription

1 US-Japan Workshop on Heavy Ion Fusion and High Energy Density Physics at Utsunomiya University Semi-empirical Studies of Warm-Dense-Matter Physics using Fast Pulse Power Device Toru Sasaki, Yuuri Yano, Mitsuo Nakajima, Tohru Kawamura, and Kazuhiko Horioka Department of Energy Sciences Tokyo Institute of Technology contact us:

2 Background HIF(Heavy Ion Fusion) Scenario --- Heavy Ion Beams have to irradiate the pellet surface and uniformly deposit the drive energy. Fluctuation of deposition energy and/or pressure should be less than a few % for ignition and high gain. Estimate and Measure Warm Dense State (ex. EOS, Transport Coefficient, Stopping Power) Heavy Ion Beam Fuel Pellet Beam Irradiation Implosion Phase HIF Concept(Direct Irradiation) Ignition Phase

3 Warm Dense State Features of Warm Dense State High Density and Low Temperature Debye Length < Ion Sphere Radius ( ) 1/3 ɛ k B T 3 λ D = a = ne 2 4πn Electrons in High Degeneracy θ = E kin E F = k B T 2 2m e (3π 2 n) 2/3 Coupled Plasma State --- Γ > 1 Γ = E pot E kin = (Z e) 2 4πɛ a k B T Density-Temperature Diagram

4 Advantages of the Discharge Produced Plasma Wire Discharges in Water Ease of Generation. Axial Symmetry. Ease of Evaluation of Conductivity and Input Energy History by Voltage and Current. Tamper Effect. Transparent. Can compare the hydrodynamic behavior with 1-D Magneto Hydrodynamic(MHD) simulation.

5 Remark of This Study Fit the numerical shock and contact surface trajectories to the experimental ones. Evaluate the Equation of State(EOS) models and transport coefficients using Semi-empirical fitting of hydrodynamic behavior. Evaluate EOS and transport coefficients in broad density-temperature range.

6 Experimental Setup Experimental Set-up Load Section Filled with Water Tamper Effect Transparent Plasma Boundary Shock Wave Behavior Low Inductance by Coaxial Circuit Wire Experimental Arrangement Picture of Load Section Charge Voltage: 1kV C: 3.2μF Circuit Inductance: 13nH Load: Al, Cu and W Wire (ψ=1um)

7 Typical Waveforms Typical Waveforms for Wire Discharges 25 2 Voltage Current 25 Current Voltage Current Al 2 Cu 15 Voltage W 2 Voltage[kV] and Current[kA] The current waveform has sharp peak at starting phase. The voltage waveform depends on the wire materials. Waveforms are reproducible.

8 Definition of Evaporation Timing Resistance[Ω] 1 2 Same Resistance Comparison of Resistance and Input Energy History for Al-Wire Liquid-Vapor Phase Transition 15kV Φ=1µm with Tamper 1kV Φ=1µm with Tamper Energy[J] Liquid-Vapor Phase Transition 15kV with Tamper 1kV without Tamper 1kV with Tamper Initial Resistans Time[ µs] 1kV Φ=1µm without Tamper Vaporization Energy 5.15J Time[ µs] The evolutions of resistance didn t depend on the discharge condition until 2ns. The input energy exceeded the vaporization energy at 2ns. (With Tamper means in Water, Without Tamper means in Air.)

9 Evolution of Input Energy Comparison of Input Energy History Energy[J] Liquid-Vapor Phase Transition Cu Al 3 W Time[ µs] Evolution of energy was dependent on initial resistance.

10 Evolution of Plasma Boundary Framing Photographs and Evolution of Plasma Boundary 6 5 (a) 18-19ns WireRadius[µm] Liquid-Vapor Phase Transition Cu W Al 1 Initial Radius (b) 17-18ns Framing Photos (Al:φ=1μm) Plasma Radius History Evolution of plasma radius depended on Evolution of Input Energy.

11 Evolutions of Conductivity 1 8 Initial Conductivity at Room Temperature Conductivity[S/m] Liquid-Vapor Phase Transition Dense Plasma Region Cu Al Neutral Dominant Region Cu Spitzer Time[ µs] Al Spitzer W W Spitzer Conductivity curve has a bottom at ~5ns for Al and Cu- Wire, at ~1.2us for W-Wire. About 1 times compared with Spitzer s conductivity.

12 Evaluation of Conductivity Evaluations of Conductivity for Each Wires. 1 6 Al Cu W σ[s/m] K 2K 3K 2K 3K 2K 1K 1K 1K ρ[kg/m 3 ] ρ[kg/m 3 ] ρ[kg/m 3 ] The theoretical model [1] coincides with our results at high temperature. The low temperature(1k) region can t be explained by the conventional model. Wide parameter region is covered using pulse-power discharges in water. [1] S. Kuhlbrodt et. al., Contrib. Plasma Phys., 45, 73(25)

13 Evolution of Coupling Parameter Evolutions of Estimated Coupling Parameter Γ = E pot = E kin (Z e) 2 4πɛ a k B T 5 4 W Γ 3 2 Cu Al Wire plasma maintains dense state up to 2μsec. Coupling parameter plateaus at Γ~2 for Al-Wire, Γ~2.5 for Cu-Wire and Γ~3 for W-Wire.

14 Evolution of Shock Wave 1.17µs 5 4 Initial Wire Radius ShockRadius[mm] Al W Cu Initial Radius Time[ µs] Shock Wave History in Water Induced by Wire Explosion 1.77µs Shadow Graph Image of Cu- Wire Explosion Evolution of shock wave in experimental results are R(t) t 1/2

15 Initial Condition Initial Condition Define Wire Conductivity by Experimentally Input Energy(Current) 25 Shock Wave Wire Setting of Equation of State(EOS)-> Water: IAPW95 [2] -> Wire: QEOS [3] or Ideal EOS [2] IAPWS Release on the IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use, IAPWS Secretariat(1996). Water Wire Water ρ=solid Density ρ=1kg/m 3 T T i =T e : Vapor i =T e =3K Temperature r wire =5µm [3] R. M. More, et. al., Phys. Fluids 31, 359 (1988) r Voltage[kV] and Current[kA] Voltage 1 2 Current

16 Comparison of Hydrodynamic Behaviors Effect of Equation of State Radius[mm] Ideal EOS Shock Surface Ideal EOS Contact Surface QEOS Shock Surface 1.5 Initial Wire Radius QEOS Contact Surface The shock and contact surface trajectories are strongly depended on Equation of State(EOS).

17 Comparison with Experimental Observation Comparison of the Numerical(QEOS) and Experimental Results 5. Al Ex. Result(Shock Wave) Cu W 4. Radius[mm] Initial Wire Radius Num. Result (Shock Wave) Ex. Result (Contact Surface) Num. Result (Contact Surface) Num. Result (Shock Wave) Ex. Result(Shock Wave) Ex. Result (Contact Surface) Num. Result (Contact Surface) Num. Result (Shock Wave) Ex. Result(Shock Wave) Ex. Result (Contact Surface) Num. Result (Contact Surface) Discrepancy of the hydrodynamics indicates the requirement of more accurate EOS model.

18 Summary The theoretical model for conductivity can explain the experimental results at high temperature region. However, results at low temperature region indicate the requirement of more accurate model for the prediction of the plasma temperature and EOS. Observed discrepancy of the numerical and the experimental behaviors of the hydrodynamics indicates the requirement of more accurate EOS at Warm Dense region. The semi-empirical fitting of the contact surface and the shock wave evolution accompanied with the exploding wire discharges in water is proposed for the studies of plasma at Warm Dense State. Because, the hydrodynamic behaviors are strongly affected by the EOS models.