Since one of the most valuable measurable parameters in laser, called effective cavity lifetime, gives useful information about laser, this paper aims to study the description of it dependency, τ_(ph)~(eff), on geometrical characteristics of N_2-laser, electrodes length and amplifier gap separation. First based on the studies carried out on it, an oscillator-amplifier laser is used which operates under moderate current density conditions; Then in order to obtain a theoretical relation for effective cavity lifetime and to demonstrate the mentioned dependency using rate equations, at first a one-dimensional method is used for the photon density. Since the answers of rate equations in an oscillator-amplifier laser are complicated, a single-oscillator based modelis offered to make rate equations simpler. In this model, at first it is supposed that the photon density of inner part of the amplifier could ben_(ph) (z,t)= n_(ph) (0,t) exp (g_0(z)z), If n_(ph)(approx=) n_(ph) (z,t), then rate equations are used for this density and since g0 is a function of z or amplifier electrode length (Z(approx=)l_(AMP)), the cavity effective life time is calculated for equivalent oscillator. Then, Since most of studies carried out in one dimension, so for approaching to more actual system a two -dimensional method is used for the photon density. So, we consider Z andY, which Z is along amplifier electrodes length and Y is along gaps separation. Supposing that Z and Y are independent on the photon density, two independent relations can be considered for the photon density. In this step, 2-dimensional photon density could be regarded as:nph (z,y,t) = n_(ph) (z,t) n_(ph_ (y,t) and then 2-dimensional effective cavity lifetime amount is obtained as: (τ_(eff)~(ph)~(-1) = c/l_(AMp)(1 +γ_l~z + bl_(AMp)γ_1~z) + c/d_(AMp)(γ_l~Y + ad_(Amp)γ_1~y), This relation includes 2 independent values along the electrodes length (Z(approx=)l_(AMP)) and gap separation (y(approx=)d_(AMP)). It also demonstrates that the obtained 2-dimentional relation represents a perfect schema for lifetime behavior. The results of this calculation are consistent with other reported N2-laser effective cavity lifetime values measured under moderate current density conditions.
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机译：由于激光中最有价值的可测量参数之一（称为有效腔寿命）可以提供有关激光的有用信息，因此本文旨在研究τ_（ph）〜（eff）对N_2激光的几何特性的依赖性，电极长度和放大器间隙分离。首先，基于对它的研究，使用了振荡器-放大器激光器，该激光器在中等电流密度条件下工作。然后，为了获得有效腔寿命的理论关系并使用速率方程式证明所提及的依赖性，首先，将一维方法用于光子密度。由于振荡器-放大器激光器中速率方程的答案很复杂，因此提供了基于单振荡器的模型来简化速率方程。在该模型中，首先假设放大器内部的光子密度可以为n_（ph）（z，t）= n_（ph）（0，t）exp（g_0（z）z），如果n_ （ph）（approx =）n_（ph）（z，t），则将速率方程式用于此密度，并且由于g0是z或放大器电极长度（Z（approx =）l_（AMP））的函数，因此计算等效振荡器的腔有效寿命。然后，由于大多数研究是在一维的，所以为了接近更实际的系统，对光子密度使用二维方法。因此，我们考虑Z和Y，其中Z沿放大器电极长度，Y沿间隙间隔。假设Z和Y与光子密度无关，则可以考虑两个独立的关系作为光子密度。在此步骤中，二维光子密度可以视为：nph（z，y，t）= n_（ph）（z，t）n_（ph_（y，t），则二维有效腔寿命为获得为：（τ_（eff）〜（ph）〜（-1）= c / l_（AMp）（1 +γ_l〜z + bl_（AMp）γ_1〜z）+ c / d_（AMp）（γ_l〜Y + ad_（Amp）γ_1〜y），该关系包括沿电极长度（Z（approx =）l_（AMP））和间隙间距（y（approx =）d_（AMP））的2个独立值。获得的二维关系表示寿命行为的理想方案，该计算结果与其他报道的在中等电流密度条件下测得的N2激光器有效腔寿命值一致。
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