The Theory Of Formation Process Of Magnetically Insulation Without Space-electron Loss

Since CTBT was signed in 1996,Above Ground Experiments have become a focus in nuclear weapon states.At the end of last century,the Sandia National Laboratory of the United States found that using the fast Z-pinch driving wire array,the condition of high energy density physics required by the nuclear explosion simulation could be obtained and the fusion ignition could be achieved in a relatively economical manner.So the design of large fast Z-pinch facility has become a focus in the area of pulse power technology. Magnetically Insulated Transmission Line(MITL),functioning as conflux and transmission of pulse power,is a key component in fast Z-pinch facility.Because electrons emitting from cathode are prevented to reach at anode by magnetic-field produced by linear-current of MITL,the power flow in MITL can still transmit ahead with flow density up to TW/cm² level.The model of the MITL is different from that of vacuum transmission line.The theories of MITL,which include magnetic-insulation steady state model and magnetic-insulation formation process model,occurred early in 1921 and developed between 1970s and 1990s.These theories mainly study the tracks of electron in gap of MITL during magnetically insulated transmission.These theories have been used not only to explain the phenomena of magnetic-insulation transmission but also to construct MITL circuit model.However,these theories can not resolve the following problems in MITL circuit modeling:(1) how to compute the distribution parameters of magnetically-insulated steady state circuit model;and(2) how to compute the change of linear-current and -voltage caused by magnetically-insulated formation process without space electron loss.This paper focuses on these two problems.Firstly,this paper constructs a variable space(h₂,C₁,γ) basing on the laminar flow model of Creedon which is a theory of magnetically-insulated steady state,and then the analytic equations of distributions of electromagnetic field,charge density and current density under magnetically-insulated steady state in the gap of MITL are described in the variable space.However,the model of Creedon does not construct such a variable space,nor give the distribution equations of these parameters.Using these distribution equations,this paper obtained these curves of distributions of electromagnetic field and so on in the gap of Z-accelerator MITL.Moreover,by using these distribution equations,this paper proves that the laminar flow model of Creedon is consistent physically with that of Mendel which was deduced from the arbitrary momentum model of Mendel and widely used in engineering. Mendel's thought of arbitrary momentum model of magnetically-insulated steady state is completely different from that of Creedon's laminar flow,so whether there was different between the laminar flow model of Mendel and that of Creedon is still a problem for a long time.Secondly,with these analytic equations of electromagnetic field and so on,this paper computes distributed-inductance and -capacitance in MITL circuit model of magnetically-insulated steady state.It finds that,contrary to vacuum transmission state which geometry boundaries of current loop and charge distribution zones are fixed,the geometry boundaries of linear-current loop and linear-charge distribution zones under magnetically-insulated steady state are varied.Therefore,this paper defines the distributed-inductance and -capacitance of magnetic-insulation steady state with tensor,and explains the relationship of distributed-inductance and -capacitance between the state parameters of magnetically-insulated steady state and the geometry of the distribution zones of current loop and charges.However,since the tensors of distributed-inductance and -capacitance can not simplify the circuit model,this paper defines also equivalent-distributed-inductance and -capacitance to simplify the circuit model.The similar investigations are not found in the existing lectures.The final problem addressed in this paper is to determine the quantitative relationship between the linear-voltage and -current at start and terminal time during magnetic-insulation formation process of without electron loss.Formation of magnetic-insulation is a transition between vacuum transmission state and magnetic-insulation steady state,including formation processes with electron loss and that without electron loss.The formation process without electron loss occurs often in the load-limited MITL which length is extremely shorter than the pulse length and the linear-current are very large.Investigation the magnetic-insulation formation process without electron loss could be of great importance for design of MITL. This paper studied the relationship of exchange between the space-electron kinetic energy and electromagnetic-field energy during the magnetic-insulation formation process,and then derives an equation on the total kinetic energy of space-electrons which exit in the whole process and an equation on the changes of total energy of electromagnetic field on MITL cross-section during the process.By these equations,this paper presented a new model of magnetic insulation formation process without electron loss,and then the change of linear-voltage and -current at the start and end time of the formation process was determined. This paper validates the model by three phenomena observed in Z accelerator's MITL,and the simulation results are well consistent with those phenomena.The existing magnetic insulation formation model can not determine the change of linear-current and -voltage caused by magnetic insulation formation process without electron loss.