Breakdown voltage and Paschen's law

    The conditions for self-sustained discharge are:

    After the discharge changes from non-self-sustaining to self-sustaining, not only the characteristics of the discharge undergo a qualitative change (from relying on external factors to internal factors), but the discharge current will also increase significantly as a result, and the discharge will change from dark to bright. Therefore, the sudden transition from non-self-sustained discharge to self-sustained discharge is usually called breakdown (or fire, ignition, rupture).

    The condition for breakdown to occur is the multiplication factor Q=1 given by the above formula. Under the conditions of the discharge tube structure parameters, internal gas composition and pressure, the multiplication factor Q is directly related to the voltage between the electrodes, that is, the discharge breakdown occurs only when the voltage between the two electrodes of the discharge tube increases to a certain value.

    The inter-electrode voltage that causes the gas to break down is called the breakdown voltage (or ignition voltage, burst voltage) Vs of the discharge. The calculation formula of breakdown voltage is:

    Analyzing the above formula, it can be seen that A and B are parameters related to the gas type; although γ is related to the electric field strength, it has little effect after taking the second logarithm; therefore, the breakdown voltage Vs is mainly affected by the gas pressure p and The influence of the pole spacing d. However, Vs does not vary with p and d respectively, and the surface is a function of the product pd of the two. That is, Vs=f(pd).

    In 1889, Paschen first obtained the above-mentioned relationship in the laboratory. Therefore it is called Paschen's law, and the above formula is called Paschen's formula.

    According to Paschen’s formula, the relationship curve between Vs and pd as shown in the figure can be drawn, which is called Paschen curve. The Paschen curve can also be obtained through experiments, and its shape is the same. It can be seen from the curve in the figure that Vs first decreases with the increase of pd, and when it reaches a minimum value, it increases with the increase of pd. That is, Vs has a minimum value at a certain pd value. The appearance and determination of this minimum breakdown voltage (Vs) min is a very important rule. In practical applications, it is usually desirable to reduce the breakdown voltage of the gas discharge.

    The breakdown voltage directly depends on the values of a and γ. In addition to the relationship between Paschen's law and pd, γ is also related to the surface condition of the cathode material and the electrode structure; and α depends on the composition of the gas. Different gas components, different A and B constants, have different breakdown voltages. The mixing of different gases can also change the value of Vs.

    The discharge phenomenon in the mixed gas is very common in vacuum engineering, such as the mixing of the vapor of the metal to be smelted (or evaporated) and the residual gas, the mixing of the inert working gas and the active reaction gas filled in the reactive sputtering coating, and so on. If the conditions of the Penning effect are satisfied between the two mixed gases, the breakdown voltage of the gas will decrease; if the mixed gas is a gas that easily adsorbs electrons to form negative ions, or a molecular gas, the breakdown voltage will generally increase.

    The nature and form of the discharge formed after a fire is related to many conditions. The main conditions are the nature of the gas, the pressure of the gas, the shape of the electrode, the distance between the electrodes, the size of the applied voltage, and the power of the external power supply. However, it cannot be simply assumed that a certain discharge form can be obtained by selecting certain conditions.

    Because the discharge conditions are also related to the current density emitted by the cathode during discharge, and so on, it is related to the cathode temperature and electron emission. Therefore, different discharge properties and forms can be obtained by different ignition methods. For example, when slowly increasing the voltage between two electrodes placed at a certain distance from each other in the middle of the vacuum, firstly, a glow discharge is obtained, and then a transition to an arc discharge is obtained. But if the two electrodes are brought into contact with each other first, and then they are pulled apart, the arc discharge can be obtained directly, such as the arc ignition of vacuum electric arc furnace and multi-arc ion coating machine. If the voltage between the two electrodes is high and the power of the power supply is small, a spark discharge is formed.

(Huiputech)