A comparison between a self-consistent nonlinear theory of current modulation and 2D particle in cell simulation in two-cavity RKA
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摘要: 采用一维自洽束波互作用的非线性理论，探索了相对论速调管放大器(RKA)的束流调制特性，并与二维PIC结果进行了比较和分析。首先推导了环形电子束的几何因子，然后分别给出了两腔调制时归一化调制电流和电子束动能的积分微分方程。采用调制电子束激励中间腔的非线性理论估算了中间腔间隙电压的幅度和相位，幅度的相对误差为0.07%，相位误差为2.15°。给出了输入腔和中间腔的间隙耦合系数公式，对于束压为715.2 kV、束流为8 kA的电子束，当输入腔和中间腔间隙电压分别为14，315.2 kV，输入腔和中间腔相位差为90.59°时，采用一维非线性理论和二维粒子模拟程序分别计算了基波电流调制系数和距离的关系。对于基波电流调制系数，中间腔之前处于线性区，理论值与模拟值比较一致；在中间腔内部基波电流调制系数出现明显的下降，理论值与模拟值之间的差距较大；中间腔之后处于非线性区，对于基波电流调制系数的最大值和对应的纵向位置，理论值与模拟值基本一致。当束流传输距离为65.8 cm时，计算了归一化电流和归一化电子束动能随时间的变化和电荷守恒参量N(z)与调制电流的n次谐波的电流调制系数随传输距离的变化情况。Abstract: In this paper, first the geometrical factor is derived and the integrodifferential equation of the instantaneous current and the beam kinetic energy in two-cavity klystrons is given. Then a nonlinear theory of cavity excitation by modulated electron beam is applied to calculate the amplitude and the phase of the gap voltage of the middle cavity, the relativistic error of the amplitude is 0.07%, the error of the phase is 2.15°. The coupling coefficient of the gap of the coaxial cavity is obtained. With electron beam voltage of 715.2 kV, electron beam current of 8 kA, and the gap voltages of the input cavity and the middle cavity of 14 kV and 315.2 kV respectively, the fundamental harmonic current modulation coefficient versus distance z is calculated by both the two dimensional particle in cell (PIC) simulation and the code of nonlinear theory. The results of the theory and the simulation agree remarkably well. With the beam propagation distance of 60.8 cm, the fundamental harmonic current modulation coefficient and the kinetic versus the normalized time are calculated, the normalization constant and the nth harmonic current modulation coefficient versus distance z are also calculated.
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图 3 基波电流调制系数C1与距离z的关系图
Figure 3. Fundamental harmonic current modulation coefficient C1 versus distance z
图 4 归一化动能K(ζ, θ)和归一化电流F(ζ, θ)与归一化时间θ的关系图
Figure 4. Normalized kinetic energy K(ζ, θ) and normalized current F(ζ, θ) versus normalized time θ
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