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我们在Geant4(Geometry and Tracking 4)框架[33]下,构建了探究负离子穿越Al2O3微孔膜的理论模型[31]。其中主要构建并编写了以下物理过程的程序:镜像电荷作用、沉积电荷作用、散射过程和电荷交换过程,具体细节见我们之前的工作[31]。我们在计算中设置:单次粒子穿越单个微孔过程完成后,在微孔膜的轴向发散度内进行一次随机摆动,来精确重现微孔膜中孔的轴向发散情况。为简化计算过程,我们对整个体系进行了坐标变换[31],离子在微孔中的动量方向可表示为
$ {\vec p_{\rm{c}}} = \left( {\begin{array}{*{20}{c}} {{\rm{cos}}{\varphi _{\rm{d}}}{\rm{cos}}{\theta _{\rm{d}}}{\rm{cos}}\psi - {\rm{cos}}{\varphi _{\rm{d}}}{\rm{sin}}{\theta _{\rm{d}}}{\rm{sin}}\psi }&{ - {\rm{sin}}{\varphi _{\rm{d}}}}&{{\rm{cos}}{\varphi _{\rm{d}}}{\rm{cos}}{\theta _{\rm{d}}}{\rm{sin}}\psi + {\rm{cos}}{\varphi _{\rm{d}}}{\rm{sin}}{\theta _{\rm{d}}}{\rm{cos}}\psi }\\ {{\rm{sin}}{\varphi _{\rm{d}}}{\rm{cos}}{\theta _{\rm{d}}}{\rm{cos}}\psi - {\rm{sin}}{\varphi _{\rm{d}}}{\rm{sin}}{\theta _{\rm{d}}}{\rm{sin}}\psi }&{{\rm{cos}}{\varphi _{\rm{d}}}}&{{\rm{sin}}{\varphi _{\rm{d}}}{\rm{cos}}{\theta _{\rm{d}}}{\rm{sin}}\psi + {\rm{sin}}{\varphi _{\rm{d}}}{\rm{sin}}{\theta _{\rm{d}}}{\rm{cos}}\psi }\\ { - {\rm{sin}}{\theta _{\rm{d}}}{\rm{cos}}\psi - {\rm{cos}}{\theta _{\rm{d}}}{\rm{sin}}\psi }&0&{ - {\rm{sin}}{\theta _{\rm{d}}}{\rm{sin}}\psi + {\rm{cos}}{\theta _{\rm{d}}}{\rm{cos}}\psi } \end{array}} \right) \cdot \left( {\begin{array}{*{20}{c}} {{\rm{sin}}{\theta _{\rm{m}}}{\rm{sin}}{\varphi _{\rm{m}}}}\\ {{\rm{sin}}{\theta _{\rm{m}}}{\rm{cos}}{\varphi _{\rm{m}}}}\\ {{\rm{cos}}{\theta _{\rm{m}}}} \end{array}} \right),$ (1) 式中:θm为束流发散度;φm为0到2π上的均匀分布函数;ψ是相对于束流方向的微孔倾角;θd是微孔轴向发散;φd是在0到2π上的均匀分布函数。
当带电粒子与绝缘体表面间距足够小时,会在绝缘体表面产生极化作用,绝缘体内部的异种电荷受到吸引,而同种电荷受到排斥,从而产生镜像电荷作用,吸引带电粒子向绝缘体表面靠近。在一个理想的圆柱内部,镜像电势可以表示为[34-35]
$$V(\rho ) = - \frac{{\varepsilon - 1}}{{\varepsilon + 1}}\frac{{q{\rho ^2}}}{{2a({a^2} - {\rho ^2})}},$$ (2) 其中:a是圆柱半径;ρ是离子距圆柱轴心的距离;ε为材料的介电常数;q为入射粒子电荷量。
在计算模型中,电荷的沉积是由负离子与微孔内壁的几何碰撞造成。为加速沉积电荷产生的电场计算,我们将微孔内壁切割为微小的矩形结构。由带电矩形产生的电势的表达式[12]为
$U = {\sigma _0}a\ln \left[ {\frac{{z - {z_{\rm s}} + \sqrt {{{(x - {x_{\rm{s}}})}^2} + {{(y - {y_{\rm{s}}})}^2} + {{(z - {z_{\rm{s}}})}^2}} }}{{z - {z_{\rm s}} - {L_0} + \sqrt {{{(x - {x_{\rm{s}}})}^2} + {{(y - {y_{\rm{s}}})}^2} + {{(z - {z_{\rm{s}}} - {L_0})}^2}} }}} \right],$ (3) 式中:σ0是带电矩形的表面电荷密度; a和L0是微条的宽和长; xs, ys和zs是矩形的空间位置。
粒子在遭遇近距离碰撞时,只有部分粒子可以从物质表面散射[36-37]出来,其概率的表达式[31]为
$${P_{\rm{R}}} = {{\rm{e}}^{\frac{{ - E{{\sin }^2}\theta }}{{2\pi {Z_{\rm{t}}}{Z_{\rm{p}}}{n_{\rm{a}}}{a_{\rm{s}}}\sum\limits_{{d_{\rm{i}}}}^3 {\frac{{{c_i}}}{{{d_{\rm{i}}}}}} {{\rm{e}}^{ - Z{d_i}/{a_{\rm{s}}}}}}}}},$$ (4) 其中:E是入射离子的动能;θ是离子碰撞到物质表面时的入射角度;Z是入射离子电荷态;Zt和Zp分别是靶原子和入射离子的核电荷数;na是微孔内表面的原子数密度;ci和di是常数(ci={0.35,0.55,0.1}, di={0.3,1.2,6}),as为
$${a_{\rm{s}}} = {\left( {\sqrt {{Z_{\rm{t}}}} + \sqrt {{Z_{\rm{p}}}} } \right)^{ - 2/3}}{\text{。}}$$ (5) 散射过程中的入射与出射角度遵循Firsov散射公式分布[31],出射概率最大的角度与入射角一致。
遭遇近距离碰撞散射的粒子会转化为Cl+离子、Cl0和Cl–离子。根据Al2O3能带结构[38]可知,在单次碰撞中,Cl–离子经过一次电荷态交换后转化为Cl0,然后部分Cl0再经一次电荷态交换才能转化为Cl+离子。而粒子经二次及以上近距离碰撞出射的几率要远小于经一次碰撞出射的几率。在这个能区下Cl–离子经近距离碰撞转化为Cl0和Cl+离子的几率接近于1,而Cl+在后续的近距离碰撞之下转化为Cl0的几率接近于1[39-40]。
因此,我们设定Cl–离子在一次碰撞时以一定的散射几率
$P_{\rm{R}}^{}$ 转化为Cl0、Cl+,转化概率分别为$P_{\rm{R}}^{}{P_1}$ ,$P_{\rm{R}}^{}{\rm{(1 - }}{P_1})$ 。而在二次碰撞中,Cl0以$P_{\rm{R}}^{}$ 的几率保持电荷态不变,转化为其他粒子的几率为0;而Cl+离子转化为Cl0的几率为$P_{\rm{R}}^{}$ ,转化为其他粒子的几率为0。
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摘要: 理论模拟结合实验研究了16-keV Cl-离子穿越不同厚度(7和12 μm)的Al2O3微孔膜的物理过程,发现负离子传输中并不存在与正离子传输类似的明显的导向现象。在只考虑散射过程的情况下,模拟出的穿透粒子角分布及电荷态分布与实验结果符合很好,出射的Cl-离子沿初束方向分布;Cl0、Cl+离子沿微孔轴向分布。仔细分析了不同出射粒子的角分布,发现出射的Cl+在微孔轴向与初束方向之间分布;经单次散射出射的Cl0沿微孔轴向分布,而经多次散射出射的Cl0向初束方向移动。发现了Cl-离子穿越不同厚度的具有相同微孔直径的Al2O3微孔时,较厚的膜出射的Cl+/Cl0比例低。理论分析显示,这是由散射过程的特性造成的,随着微孔膜厚度的增加,出射的Cl0中经单次碰撞的比例变小,而多次散射出射的比例增加,从而导致Cl+离子转化为Cl0的几率要远大于Cl0转化为Cl+离子的几率,使得长的微孔出射的粒子中Cl+/Cl0比例低。Abstract: The transmission of 16-keV Cl– ions through Al2O3 nanocapillaries of 7 and 12 μm in thickness was studied both by experiment and simulation. It is found that the transmission of negative ions is different from that of positive ions through insulating nanocapillaries, where the deposited charges result in the so-called guiding effect. For the case of only the scattering, the transmitted angular distributions and charge state distributions from the simulations agreed well with the experimental results, i.e., the transmitted Cl– ions exits to the direction of the primary beam; the transmitted Cl0 and Cl– spread around the axis of the capillaries. The analysis of the simulated trajectories shows that the transmitted Cl+ ions spans from the axis of nanocapillaries to the primary beam direction; the transmitted Cl0 due to the single scattering is centered around the axes of the nanocapillaries while the transmitted Cl0 through multiple scattering shifts to the direction from the axes of the capillaries to the primary beam direction. From the simulations, it is found that the ratio of Cl+/Cl0 for the transmitted particles exited from the nanocapillaries of longer lengths is lower, in accord to the experiments. The increase of the length of the capillaries will lead to the drop of the portion of transmitted Cl0 by single scattering and the increase of the probability of the exiting of Cl0 through multiple scatterings. Therefore the probability of Cl+ ions changed to Cl0 is much larger than that Cl0 changed to Cl+ ions in the collision process, leading to the smaller ratio of Cl+/Cl0 for the transmitted particles exited from the nanocapillaries of longer lengths.
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Key words:
- Cl– ion /
- insulating nanocapillaries /
- scattering process
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图 4 (在线彩图)16-keV Cl–离子在倾角0.6°下穿越厚7 μm的 Al2O3微孔膜的角分布和电荷态分布[31]
(a)实验角分布;(b)计算角分布;(c)实验电荷态分布;(d)计算电荷态分布。
图 5 (在线彩图)16-keV Cl–离子穿越不同厚度的微孔膜后,穿透的Cl0峰位置随倾角变化关系
黑色和红色三角形分别表示厚7 μm的微孔膜的实验结果与计算结果[31],黑色和红色圆圈分别表示厚12 μm的微孔膜的实验结果与计算结果。实线表示函数Y=X。
图 6 (在线彩图)16-keV Cl–离子分别穿越7与12 μm厚的Al2O3微孔膜后的Cl+/Cl0在不同倾角ψ下实验与计算比例
黑色实心三角形和红色空心三角形分别为穿越厚7 μm的微孔膜的Cl+/Cl0实验结果和计算结果[31];黑色实心圆形与红色空心圆形分别为穿越厚12 μm的微孔膜的Cl+/Cl0实验结果与计算结果。
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