**3.2 Magnetically driven quasi-isentropic compression**

The techinques to realize magnetically driven quasi-isentropic compression are based on all kinds of pulsed power generators, such as ZR, Veloce[29], Saturn[30] facilities. As shown in Fig.9, Current *J* flowing at the anode and cathode surfaces induces a magnetic field *B* in

Fig. 9. Experimental configuration of samples for magnetically driven quasi-isentropic compression

Magnetohydrodynamics of Metallic Foil Electrical

and measuring probe (b).

Fig. 11. The loading pressure histories of CQ-1.5

Explosion and Magnetically Driven Quasi-Isentropic Compression 359

(a) (b)

Fig. 10. The picture of experimental apparatus CQ-1.5 (a) and its load area including sample

**4. MHD simulation of metallic foil electrically exploding driving highvelocity** 

The code used to simulate the electrical explosion of metallic foil is improved based our SSS code[32], which is one dimensional hydrodynamic difference code based on Lagrange orthogonal coordinate. For the case of electrical explosion of metallic foil, the power of Joule

**flyers and magnetically driven quasi-isentropic compression** 

**4.1 Metallic foil electrically exploding driving highvelocity flyers** 

Fig. 11. shows the typical loading pressure histories. The pressure is a ramp wave.

the gap. The resulting *J B* Lorentz force is transferred to the electrode material, and a ramp stress wave propagates into the samples. The stress normal to the inside surfaces of electrods is <sup>2</sup> <sup>0</sup> (1 2) *P J <sup>B</sup>* , where *J* is the current per unit width. Two identical samples with a difference in thickness of *h*, are compressed by identical B-force and their particle velocity profiles *u*(*t*) are measured by DISAR or VISAR.

An inverse analysis technique, i.e, the backward integration technique using difference calculation is developed to extract a compression isentrope from free-surface or windowinterface velocity profiles[31]. Different from Lagrangian wave analysis, inverse analysis can account for ramp-wave interactions that arise at free surfaces or window interfaces. In this method, the profiles of velocity and density are specified as an initial condition at the Lagrangian position of the measurement, then the equations of motion from equation (5) through equation (7) are integrated in the negative spatial direction to a position inside the material that is free of interaction effects during the time of interest. Assuming some parametric form shown in equation (8) for the mechanical isentrope of the material such as Murnaghan euqation or others, the parameter values are found by iteratively performing backward intergration on data from multiple thickness of the sample while minimizing the deviation between the results at a common position.

$$
\sigma(\text{h} - \text{d}\text{h}, t) = \sigma(\text{h}, t) + \rho\_0[\text{u}(\text{h}, t + \text{d}t) - \text{u}(\text{h}, t - \text{d}t)] \text{dh} \,/\, (2 \, \text{d}t) \tag{5}
$$

$$\varepsilon(\mathbf{h} - \mathbf{d}\mathbf{h}, \mathbf{t}) = F[\sigma(\mathbf{h} - \mathbf{d}\mathbf{h}), \mathbf{t})] \tag{6}$$

$$
\ln(h - \text{d}h, t) = \ln(h, t) + [\varepsilon(h, t + \text{d}t) - \varepsilon(h, t - \text{d}t)] \text{d}h \text{ / (2d}t) \tag{7}
$$

$$B\_s(V) = B\_{s0} \left(\frac{V\_0}{V}\right)^B \tag{8}$$

In order to do quasi-isentropic compression experiments, a compact capacitor bank facility CQ-1.5[13] was developed by us, which can produce a pulsed current with peak value of about 1.5 MA and rising time of 500 ns~800 ns. The solid insulating films are used to insulate the anode electrode plates from the cathode ones. And the facility is used in the air. Fig.10 presents the picture of CQ-1.5.Based on CQ-1.5, about 50 GPa pressure is produced on the surface of steel samples. The parameter values of CQ-1.5 is given in Table 3.


Table 3. The specifications of CQ-1.5

ramp stress wave propagates into the samples. The stress normal to the inside surfaces of

a difference in thickness of *h*, are compressed by identical B-force and their particle velocity

An inverse analysis technique, i.e, the backward integration technique using difference calculation is developed to extract a compression isentrope from free-surface or windowinterface velocity profiles[31]. Different from Lagrangian wave analysis, inverse analysis can account for ramp-wave interactions that arise at free surfaces or window interfaces. In this method, the profiles of velocity and density are specified as an initial condition at the Lagrangian position of the measurement, then the equations of motion from equation (5) through equation (7) are integrated in the negative spatial direction to a position inside the material that is free of interaction effects during the time of interest. Assuming some parametric form shown in equation (8) for the mechanical isentrope of the material such as Murnaghan euqation or others, the parameter values are found by iteratively performing backward intergration on data from multiple thickness of the sample while minimizing the

0

 

( d , ) ( . ) [ ( , d ) ( , d )]d /(2d ) *h h t ht u h t t u h t t h t*

 

0

*V*  '

*B*

*uh ht uht ht t ht t h t* ( d , ) ( , ) [ ( , d ) ( , d )]d /(2d )

In order to do quasi-isentropic compression experiments, a compact capacitor bank facility CQ-1.5[13] was developed by us, which can produce a pulsed current with peak value of about 1.5 MA and rising time of 500 ns~800 ns. The solid insulating films are used to insulate the anode electrode plates from the cathode ones. And the facility is used in the air. Fig.10 presents the picture of CQ-1.5.Based on CQ-1.5, about 50 GPa pressure is produced

> rise time 500~800 ns total inductance about 18 nH total resistance ~10 m charging voltage 75 kV~80 kV peak current ≥1.5 MA

<sup>0</sup> ( )

*s s <sup>V</sup> BV B*

on the surface of steel samples. The parameter values of CQ-1.5 is given in Table 3.

performance parameters values total capacitance 15.88 F period in short-circuit 3.40 s

Lorentz force is transferred to the electrode material, and a

( d , ) [ ( d ), )] *h ht F h h t* (6)

(8)

(5)

(7)

, where *J* is the current per unit width. Two identical samples with

the gap. The resulting *J B*

<sup>0</sup> (1 2) *P J <sup>B</sup>* 

electrods is <sup>2</sup>

profiles *u*(*t*) are measured by DISAR or VISAR.

deviation between the results at a common position.

Table 3. The specifications of CQ-1.5

Fig. 10. The picture of experimental apparatus CQ-1.5 (a) and its load area including sample and measuring probe (b).

Fig. 11. shows the typical loading pressure histories. The pressure is a ramp wave.

Fig. 11. The loading pressure histories of CQ-1.5
