Oscillation properties of ion channel during long-range propagation of electron beam
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摘要: 离子通道可以有效抑制电子束在等离子体环境内传输过程中的径向扩散，已有工作研究了离子通道对电子束的影响，但离子通道建立过程和暂态特性研究则更有助于理解和利用离子通道在电子束长程传输中的作用。本文利用PIC方法对离子通道的时空分布进行二维模拟，并基于单粒子理论推导出描述离子通道振荡的解析模型，对上述两种模型的结果相互校验。上述模型的计算结果表明，在长程传输过程中，相对论电子束在等离子体内部建立的离子通道是持续周期振荡的，电子束密度、电子束初始半径以及环境等离子体密度都会对离子通道的振荡规律产生影响，针对不同的等离子体环境选择合适的电子束参数可以有效提高离子通道的稳定性，进而提升传输过程中电子束的束流质量。Abstract: It is known that the ion channel can limit the radial expansion of the electron beam during long-range propagation in the plasma environment. Previous research typically concentrated on the interaction between the beam and plasma, but research on the establishment and transient properties may lay the foundation for understanding and using the ion channel during long-range propagation. In this study, a series of 2D particle-in-cell simulations is performed and an analytical model of ion channel oscillation is constructed according to the single-particle-motion. The results show that the ion channel established by relativistic electron beam in the plasma continues to oscillate periodically during the long-range propagation of relativistic electron beam. The beam electron density, initial beam radius and the plasma density can influence the dynamics of the ion channel oscillation. Choosing suitable beam parameters based on the various plasma environment can contribute to the improvement of the stability of the ion channel and further the beam quality.
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图 3 电子束密度与等离子体密度接近（
$\varepsilon $ 较小）时离子通道的分布Figure 3. Ion channel when the beam density is close to the plasma density
图 4
$\varepsilon = 3$ 时离子通道的分布，${n_{\rm{p}}} = 6.2 \times {10^{14}}\;{{\rm{m}}^{ - 3}}$ ，${r_{{\rm{b}}0}} = 3\;{\rm{ cm}}$ Figure 4. Ion channel when
$\varepsilon = 3$ ,${n_{\rm{p}}} = 6.2 \times {10^{14}}\;{{\rm{m}}^{ - 3}}$ and${r_{{\rm{b}}0}} = 3\;{\rm{ cm}}$ 
图 5
$\varepsilon = 5$ 时离子通道的分布，${n_{\rm{p}}} = 6.2 \times {10^{14}}\;{{\rm{m}}^{ - 3}}$ ，${r_{{\rm{b}}0}} = 3\;{\rm{ cm}}$ Figure 5. Ion channel when
$\varepsilon = 5$ ,${n_{\rm{p}}} = 6.2 \times {10^{14}}\;{{\rm{m}}^{ - 3}}$ and${r_{{\rm{b}}0}} = 3\;{\rm{ cm}}$ 
图 6
${r_{{\rm{b}}0}} = 5\;{\rm{ cm}}$ 时离子通道的分布，${n_{\rm{p}}} = 6.2 \times {10^{14}}\;{{\rm{m}}^{ - 3}}$ ，$\varepsilon = 3$ Figure 6. Ion channel when
${r_{{\rm{b}}0}} = 5\;{\rm{ cm}}$ ,${n_{\rm{p}}} = 6.2 \times {10^{14}}\;{{\rm{m}}^{ - 3}}$ and$\varepsilon = 3$ 
图 7
${n_{\rm{p}}} = 6.2 \times {10^{1{\rm{5}}}}\;{{\rm{m}}^{ - 3}}$ 时离子通道的分布，${r_{{\rm{b}}0}} = {\rm{3\; cm}}$ ，$\varepsilon = {\rm{5}}$ Figure 7. Ion channel when
${n_{\rm{p}}} = 6.2 \times {10^{1{\rm{5}}}}\;{{\rm{m}}^{ - 3}}$ ,${r_{{\rm{b}}0}} = {\rm{3\; cm}}$ and$\varepsilon = {\rm{5}}$ 表 1 电子束及等离子体环境的基本初始参数
Table 1. Initial parameters of the electron beam and plasma environment
initial beam radius ${r_{ {\rm{b0} } } }$/cm initial beam energy ${E_0}$ MeV initial beam emittance ${\varepsilon _ \bot }$/（mm*mrad） $\varepsilon $ plasma density ${n_{\rm{p}}}$/${{\rm{m}}^{ - 3}}$ 3, 5 10 0.2 1～5 $6.2 \times {10^{10}}\sim 6.2 \times {10^{15}}{\rm{ }}$ 
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