Comparison between self-consistent nonlinear theory of current modulation and three-dimensional particle-in-cell simulation in multi-beam relativistic klystron amplifier
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摘要: 采用非线性理论探索了同轴多注相对论速调管放大器(CMRKA)的束波互作用特性，并与PIC结果进行了验证分析。首先推导了实心电子束的几何因子，然后分别给出了归一化调制电流和电子束动能的积分微分方程，并给出了多注速调管放大器的同轴输入腔间隙耦合系数的公式。对于束压为600 kV、束流为5 kA的16注电子束，当输入腔间隙电压分别为4.6，32.7，189 kV时，采用一维非线性理论和三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，理论和模拟结果比较一致。当间隙电压为4.6 kV时，理论计算了多注电子数的个数分别为8, 12, 16以及实心电子束的半径与单注电子束通道半径比6/15, 8/15, 10/15(通道半径不变)时基波电流调制系数随传输距离的变化。结果表明，随着多注电子数的个数和电子束半径的增加，基波电流调制系数有逐渐变大的趋势。此外还计算了当间隙电压为20 kV时，归一化电流和归一化电子束动能随时间的变化和归一化常数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。Abstract: First the geometrical factor is derived, then the integrodifferential equation of the instantaneous current and the beam kinetic energy is given, and the coupling coefficient of the gap of the coaxial cavity is obtained. With electron beam voltage of 600 kV, electron beam of 5 kA, and the gap voltage of the input cavity of 4.6, 32.7, 189 kV, and the number of the multi beam of 16, the fundamental harmonic current modulation coefficient versus distance z is calculated by the three dimensional particle-in-cell (PIC) simulation and the code of nonlinear theory respectively, the result of the theory and that of the simulation agree remarkably well. With gap voltage of 4.6 kV, the number of the multi beam of 8, 12, 16, and the ratio of the radius of solid beam and the channel of single electron beam of 6/15, 8/15, 10/15, the fundamental harmonic current modulation coefficient versus distance z is calculated by the code of nonlinear theory. With gap voltage of 4.6 kV, the fundamental harmonic current modulation coefficient and the kinetic versus the normalized time θ is calculated, normalization constant N(z) and the n-th harmonic current modulation coefficient Cn (n=1, 2, 4) versus distance z are calculated.
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图 2 腔体y-z剖面图和漂移管x-y剖面及电子束轨迹图
Figure 2. The y-z section structure of the X-band coaxial multi beam klystron (CMBK) and the y-x section structure of the drift tube
图 3 基波电流调制系数C1与距离z的关系图(ε=0.007 8, 0.056, 0.322)
Figure 3. Fundamental harmonic current modulation coefficient C1 versus distance z (ε=0.007 8, 0.056, 0.322)
图 4 基波电流调制系数C1与距离z的关系图
Figure 4. Fundamental harmonic current modulation coefficient C1 versus distance z
图 5 基波电流调制系数C1与距离z的关系图(t=6/15, 8/15.10/15)
Figure 5. Fundamental harmonic current modulation coefficient C1 versus distance z (t=6/15, 8/15.10/15)
图 6 归一化动能K和归一化电流F与归一化时间θ的关系图
Figure 6. Normalized kinetic energy K and normalized current F versus the normalized time θ
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