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首页> 外文期刊>Nuclear Instruments & Methods in Physics Research >Time dependent model of gain saturation in microchannel plates and channel electron multipliers
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Time dependent model of gain saturation in microchannel plates and channel electron multipliers

机译：微通道板和通道电子倍增器中增益饱和的时变模型

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摘要

We present and discuss a time dependent solution of the transmission line model of a channel electron multiplier, introduced in a previous paper and already solved in steady-state conditions. The model is applicable to all the situations in which the multiplier input current is sufficiently large so that the statistical variations of the gain for each electron can be ignored and it does not apply to photon counting detectors. By introducing the appropriate boundary conditions the time dependent non-linear equations of the model are reduced to an integral equation in implicit form, whose solution can be calculated numerically by a perturbative approach. In this way the multiplying current signal I(z,t) and the voltage V(z,t) are found as functions of the position z along the channel, and of the rime t during the pulse itself, for any arbitrary shape of the input current waveform. The important case of the amplification of input current pulses with a short duration compared to the multiplier recovery time is investigated in detail, showing that the non-linear behavior can be entirely described by a general function of a conveniently defined saturation parameter and that this function is characteristic of any uniform channel multiplier. The model is then used to investigate the recovery of the multiplier after a saturating pulse, and it is found that the gain recovery from weak or moderate saturation levels is exponential to a very good approximation, but with a time constant different from the characteristic time constant RC of the multiplier. Finally the case of pulses of arbitrary shape and duration is considered and examples are given of the amplification of step pulses and of a regular sequence of identical pulses. A remarkable feature of the model is that the solution can be calculated from the time shape of the output pulse, rather than from the input. This makes possible to implement methods for pulse restoration, I.e. for recovering the original input pulse shape from a measured saturated output.
机译：我们提出并讨论了通道电子倍增器传输线模型的时间相关解，该解在先前的论文中已经介绍过，并且已经在稳态条件下解决了。该模型适用于乘数输入电流足够大的所有情况，因此可以忽略每个电子的增益的统计变化，并且不适用于光子计数检测器。通过引入适当的边界条件，模型的时间相关非线性方程简化为隐式形式的积分方程，其解可以通过微扰方法进行数值计算。这样，对于任意形状的脉冲，在通道上位置z和脉冲t期间的边沿t的乘积电流信号I（z，t）和电压V（z，t）均被发现。输入电流波形。详细研究了与倍增器恢复时间相比，持续时间短的输入电流脉冲放大的重要情况，表明非线性行为可以完全通过方便定义的饱和参数的一般函数来描述，并且该函数是任何统一通道倍增器的特征。然后，使用该模型研究饱和脉冲后乘法器的恢复，发现从弱或中等饱和水平的增益恢复具有非常好的近似指数，但其时间常数不同于特征时间常数。乘法器的RC。最后，考虑任意形状和持续时间的脉冲的情况，并给出了步进脉冲和相同脉冲的规则序列的放大示例。该模型的显着特征是，可以根据输出脉冲的时间形状而不是根据输入来计算解。这使得可以实现用于脉冲恢复的方法，即用于从测量的饱和输出中恢复原始输入脉冲形状。

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