Investigation Of The Mechanism Of Space Charge Limited Current Under Multiple Fields

Electronic diode is a critical component of the apparatus that is the source of electron beams,γ-ray,X-ray,high-power microwave,thermionic energy converters and so on.The electrons emitted from the cathode of the diode have a strong space charge effect.This effect originates from the accumulation of space charges.When the space charges accumulate to a certain extent,the electric field generated by space charges will inhibit the emission of electrons from the cathode,leading to the decrease of the output current.For some low-voltage and high current diodes,such as thermionic energy converters,ions are employed to mitigate the space charge effect.For ion diodes,this paper focuses on the formation mechanism and characteristics of space charge effect influenced by initial velocities of charges edge effect,cylindrical structure,magnetic field and time-varying current.It has important reference value for the future research of high performance electronic diodes.The work and main contents of this paper are as follows:Based on Langmuir’s space charge limited current theory,the effect of the gap voltage,the initial velocity of electrons,and the positive ions on the maximum current density allowed to be transported across the gap is studied.Firstly,according to the condition in which the virtual cathode electric field is zero,the relationship between the cathode electric field and the virtual cathode potential is established.Then,based on the bipolar flow Poisson equation,the relationship between the cathode electric field,current density,and virtual cathode potential,initial velocity of electrons is are derived.It is found that after introducing ions,the maximum current density allowed to be transported across the gap increases significantly and depends on the characteristics of electrons and ions,such as the initial velocity of electrons and the emission current density of ions.In addition,the virtual cathode brings some difficulties to obtain the spatial potential distribution.We propose to take the virtual cathode as the boundary,divide the space into two parts,and calculate the corresponding potential distribution by finite difference method.The results show that in the presence of ions the space charge limited current is not directly related to the critical point at which the electron begins to reflect back,because the minimum potential is not enough to reflect the electron.This is the same as the case without ions.For the influence of the edge effect,based on the structure of the bipolar flow diode,a two-dimensional bipolar flow model with non-uniform emission is established.A numerical iteration method is proposed to simultaneously determine the unknown current density and the cathode electric field.The results show that the total limiting current is equal to that without introducing ions multiplied by a coefficient.In the presence of ions,the limiting current is also increased and depends on the structural change of diode and ion current densiy.Due to the influence of the edge effect,the limiting current of the 2D bipolar flow model is always higher than that of the 1D bipolar flow model.However,with increasing the emission width,the result of 2D bipolar flow model will gradually approach the limiting current of the1 D bipolar flow model.A bipolar flow model is established based on the cylindrical diode,and the influence of the radius of cathode and anode on the limiting current is studied.In the presence of ions,when the cathode radius is less than the anode radius,the limiting current of cylindrical diode is always greater than that of planar structure,and this difference will gradually increase with increasing the ion current density.This is because when the cathode radius is greater than the anode radius,the current density of ions decreases gradually in the process of moving towards the cathode,which reduces the maximum current density allowed to be emitted by the diode.Compared with the case without ions,the maximum current density allowed to be emitted in the cylindrical bipolar flow diode increases significantly.The increased coefficient is related to the ratio of cathode and anode radius,and to the ion current density.Consdering the influence of the magnetic and electric fields,a bipolar flow model in the plane diode is established to study the characteristics of the maximum current density allowed to be transported across the gap.The results show that when the magnetic field increases from zero to Hull cut-off magnetic field,the maximum current density allowed to be transported across the gap decreases in the form of the exponential function.This is due to the fact that the spiral motion of electrons is observed when the magnetic field is introduced,leading the transit time of electrons increasing.This will reduce the limiting current.When the ion current density is SCL,reducing the magnetic field will make the system unstable.This is because for a given ion current density,with increasing the magnetic field,the increasing rate of the maximum ratio of ion current density to electron current density is higher than that of the ratio of ion current density to electron current density.The characteristics of the space charge limited current and virtual cathode oscillation are studied with the time-varying current injection.In the space charge limited region,the output current still increases slowly with the increasing the cathode temperature,because the influence of electron initial velocity on the output current is greater than that of virtual cathode barrier on the output current.When the emission current density changes periodically,the limiting current depends not only on the gao voltage and spacing,but also on the current period.When the current period is much larger than the transit time of the electron,the limiting current only depends on the current amplitude,since the current in space is close to a constant when the current period is large enough.With decreasing the current period,the limiting current increases monotonically and gradually approaches the limiting current obtained from the time-independent model.