Theoretical Study Of Nonlinear Diffusion Wave In Electromagnetic Loading Process

Due to the rapid development of pulse power technology in the past two decades,dynamic loading of experimental samples under extreme conditions of high temperature,high pressure and high speed by using large current or strong magnetic field,has gradually become an important loading means in magnetohydrodynamics and high-pressure physics.The electromagnetic loading technique applies current and magnetic field to the surface of solid metal or plasma,and uses the Lorentz force generated by the interaction of the magnetic field with conductive fluids to drive the target.However,in this process,the current and magnetic field will simultaneously diffuse into the conductor material,causing the conductor ablation and even gasification.Especially in the extreme conditions,the diffusion process will lead to many negative problems in the magnetically driven experiments,such as the sudden and rapid leakage of magnetic flux,the ablation of metal and the fast thermoelectric ionization on the metal surface.Because in the extreme conditions,the magnetic field strength can reach thousands of Telsa,and then the strong ohmic heating effect in the conductive fluid will bring a sharp change in the resistivity of the metal conductor,which causes the phenomenon of "nonlinear magnetic diffusion wave".It has the diffusion velocity and induced current peak value far beyond the general magnetic diffusion process,and seriously affects the dynamic loading in the experimental sample.In fact,the nonlinear magnetic diffusion wave has become a key factor hindering the development of magnetically driven high energy density physics experiments.However,until now,there still exists a lack of intuitive and regular understanding on the causes,conditions and parameters of the nonlinear magnetic diffusion wave phenomenon.The sharp-front magnetic diffusion wave is a special kind of nonlinear magnetic diffusion wave.Under the background of electromagnetic loading solid metal experiments,this paper theoretically studies the sharp-front magnetic diffusion wave from numerical methods,theoretical analytical formulas,phenomenon mechanism and the resistivity model.The main research work and innovation of this paper are as follows:1.Firstly,based on magnetic flux and electromagnetic energy flow,an explicit finite volume scheme for solving magnetic diffusion problems is designed.The internal energy and magnetic energy are combined to be the "total internal energy",instead of calculating internal energy separately.This scheme is more accurate in calculating the energy transportation of nonlinear magnetic diffusion problems,and then the one-dimensional numerical simulation code is written.In order to improve the efficiency of the code,on the one hand,we design the truncated transport formula to relax the program's time step and improve the efficiency of the calculation in the strong magnetic diffusion problems,in which the resistivity distribution is extremely uneven.On the other hand,we apply the shock wave assembly method to the numerical calculation of one-dimensional sharp-front magnetic diffusion wave for the first time.Numerical examples show that the assembly method can greatly reduce the number of the program's grid and significantly improve the program's computational efficiency.2.The approximate analytical formula of sharp-front magnetic diffusion wave velocity and threshold magnetic field are revised with higher order precision.In this paper,we analyze the conservation law of flux more precisely,optimize the derivation method of approximate solution,and derive the analytical formula with higher precision.Then the modified formula is verified by comparing with the numerical computational results.The results show that the modified formulas have better estimation accuracy.3.The second type of sharp-front magnetic diffusion wave in which the boundary magnetic field strength is smaller than the threthod magnetic field strength is studied,and the corresponding formulas are derived.The existence condition of the first type of sharp-front magnetic diffusion wave is that the the boundary magnetic field strength must be larger than the threthod magnetic field strength,once the physical condition changes,the original formula for the first type of sharp-front can be no longer applicative.Therefore,we need a new research.This paper studies the characteristic properties of the second type of sharp-front magnetic diffusion wave by combining theoretical derivation and numerical simulations.The results show that the diffusion velocity of the second type is much lower than the first one,even though they have the similar distribution curve.This work improves the theory of sharp-front magnetic diffusion wave,and can be able to explain the phenomenon of the transient stagnation of magnetic flux compression process in magnetic flux compression experiments.4.By comparing and analyzing the nonlinear magnetic diffusion curves based on the step-shaped resistivity model and the Burgess resistivity model,we find they have the similar inflection point on the magnetic field distribution curvel The inflection point corresponds to the position of the current density peak in metal and can be the key identification quantity reflecting the ablation depth and magnetic diffusion rate in the magnetically driven experiments.Three metals,copper,stainless steel and tungsten,whose resistivity data have been published in literature,are used to be the calculation examples.The results show that the step-shaped resistivity model can replace the Burgess resistivity model to describe the key characteristics of the inflection point in nonlinear magnetic diffusion wave.At the end of this chapter,the idea of building the unknown step-shaped resistivity model of other metals through experiments is proposed,which can play a certain guiding role in the construction of metal's resistivity models.