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超强激光与物质相互作用产生的超热电子在物质中输运产生Kα特征线辐射和轫致辐射.Kα辐射的对比度, 即Kα特征线谱与其附近轫致辐射连续谱的强度比, 依赖于轫致辐射的方向性, 与超热电子的能量和传输相关. 本文采用蒙特卡罗模拟研究了对超热电子束有准直作用的轴向匀强磁场和高斯分布环形磁场提高铜Kα辐射对比度的可能性. 模拟和分析表明, 轴向匀强磁场无法增强轫致辐射的方向性, 不能有效提高Kα辐射的对比度. 对于高斯分布环形磁场, 当入射电子能谱具有玻尔兹曼分布时, 由于含有大量低能电子且它们的轫致辐射方向性较差, Kα辐射对比度的增幅不大; 而截掉低能部分的玻尔兹曼能谱电子束或能量较高的单能电子束入射时, 高斯分布环形磁场能大幅提高沿入射电子束后向的Kα辐射对比度. 对于能量为200—1000 keV范围的超热电子, 峰值为100 T左右的环形磁场有利于提高Kα辐射的对比度.The interaction of a high-intensity laser with a solid target generates a large number of superthermal electrons. When these superthermal electrons are transported in the target material, X-rays, including Kα line and bremsstrahlung emissions are produced. The contrast of Kα line emission, i.e. the intensity of Kα line relative to the intensity of bremsstrahlung continua around the Kα line, depends on the anisotropy of the bremsstrahlung emission and is related to the energy and transportation of the superthermal electrons. In the past, some researchers used axial or annular magnetic fields to collimate superthermal electrons, but whether these magnetic fields can enhance the contrast of Kα emission has not been studied. In the present work, the effect of an axially uniform magnetic field or an annular magnetic field with a Gaussian distribution on the contrast of Cu Kα emission is investigated by Monte Carlo simulations. The simulation results and analysis show that the axially uniform magnetic field cannot strengthen the anisotropy of the bremsstrahlung emission, so it cannot enhance the contrast of Kα emission efficiently. For the annular magnetic field with a Gaussian distribution, when an electron beam with a Boltzmann energy distribution is incident, due to the weak anisotropy of bremsstrahlung emission by low-energy electrons in the electron beam, the increase of Kα emission contrast is small. When an electron beam with a Boltzmann energy distribution, in which the low-energy part is cut off, or a mono-energetic electron beam is incident, the annular magnetic field with a Gaussian distribution significantly enhances the contrast of Kα emission in the back direction of the electron beam incidence. For an incident electron beam with an energy value in a range of 200–1000 keV, an annular magnetic field with a Gaussian distribution and a peak value of approximately 100 T is optimal for enhancing the contrast of Kα emission. Considering the existing experiments on generating annular magnetic fields and non-Boltzmann energy distribution superthermal electrons, it is possible to generate higher contrast Kα emissions with the enhancement of magnetic field in future experiments.
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Keywords:
- contrast of Kα emission /
- bremsstrahlung emission /
- magnetic field /
- Monte Carlo simulation
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图 2 $ {T_{\text{h}}} = 600{\text{ keV}} $的玻尔兹曼能量分布电子束入射产生的X射线谱
Fig. 2. X-ray spectra produced by Boltzmann distribution electron incidence with $ {T_{\text{h}}} = 600{\text{ keV}} $.
图 3 靶中无磁场(WOB)或存在$ {{\boldsymbol{B}}_{\boldsymbol{z}}} = 100{\text{ T}} $时的Kα辐射对比度 (a) $ {T_{\text{h}}} = 600{\text{ keV}} $的玻尔兹曼能量分布电子束入射; (b) $ {E_{\text{k}}} = 600{\text{ keV}} $的单能电子束入射
Fig. 3. Contrasts of Kα emission without a magnetic field (WOB) or with $ {{\boldsymbol{B}}_{\boldsymbol{z}}} = 100{\text{ T}} $ in the target: (a) Boltzmann distribution electron incidence with $ {T_{\text{h}}} = 600{\text{ keV}} $; (b) mono-energetic electron incidence with $ {E_{\text{k}}} = 600{\text{ keV}} $.
图 4 电子在z方向匀强磁场中运动示意图
Fig. 4. Schematic diagram of the motion of an electron in a z-direction uniform magnetic field.
图 5 (a) 高斯分布的环形磁场的示意图; (b) 环形磁场在x-y平面内的分布; (c) 磁场准直电子的示意图
Fig. 5. (a) Schematic diagram of an annular magnetic field with a Gaussian distribution; (b) distribution of the annular magnetic field in the x-y plane; (c) schematic diagram of the collimation of electrons by the magnetic field.
图 6 玻尔兹曼能量分布电子束入射的模拟结果 (a) $ {T_{\text{h}}} = 200{\text{ keV}} $和$ 600{\text{ keV}} $时不同方向的$ {C_{{{{\mathrm{K}}\alpha }}}} $; (b) $ \theta = {135^ \circ } $的$ {C_{{{{\mathrm{K}}\alpha }}}} $与$ {T_{\text{h}}} $的关系
Fig. 6. Simulation results of Boltzmann distribution electron incidences: (a) $ {C_{{{{\mathrm{K}}\alpha }}}} $ in different directions for $ {T_{\text{h}}} = 200{\text{ keV}} $ and 600 keV, respectively; (b) the dependence of $ {C_{{{{\mathrm{K}}\alpha }}}} $ at $ \theta = {135^ \circ } $ on $ {T_{\text{h}}} $.
图 7 单能电子束入射时的模拟结果 (a) $ {E_{\text{k}}} = 200{\text{ keV}} $和$ 600{\text{ keV}} $不同方向的$ {C_{{{{\mathrm{K}}\alpha }}}} $; (b) $ \theta = {135^ \circ } $的$ {C_{{{{\mathrm{K}}\alpha }}}} $和$ {R_{{\text{in}}}} $与$ {E_{\text{k}}} $的关系
Fig. 7. Simulation results of mono-energetic electron incidences: (a) $ {C_{{{{\mathrm{K}}\alpha }}}} $ of $ {E_{\text{k}}} = 200{\text{ keV}} $ and $ 600{\text{ keV}} $ in different directions; (b) dependence of $ {C_{{{{\mathrm{K}}\alpha }}}} $ and $ {R_{{\text{in}}}} $at $ \theta = {135^ \circ } $ on $ {E_{\text{k}}} $.
图 8 $ {T_{\text{h}}} = 600{\text{ keV}} $的玻尔兹曼能量分布的电子中能量大于500 keV的电子入射时不同探测角度的$ {C_{{{{\mathrm{K}}\alpha }}}} $
Fig. 8. $ {C_{{{{\mathrm{K}}\alpha }}}} $ at different detection angles for Boltzmann distribution electron incidence with $ {T_{\text{h}}} = 600{\text{ keV}} $ and electron energy higher than 500 keV.
图 9 单能电子束入射时, 无磁场和存在磁场$ {{\boldsymbol{B}}_\phi } $条件下的模拟结果 (a) $ {E_{\text{k}}} = 600{\text{ keV}} $时靶后表面的电子数密度分布; (b) 电子数密度分布的半高全宽与$ {E_{\text{k}}} $的关系
Fig. 9. Simulation results for mono-energetic electron incidence without a magnetic field and with $ {{\boldsymbol{B}}_\phi } $: (a) Distribution of the electron number density on the rear surface of the target for $ {E_{\text{k}}} = 600{\text{ keV}} $; (b) dependence of full width at half maximum of the distribution of the electron number density on $ {E_{\text{k}}} $.
图 10 存在不同$ {B_0} $和$ {\sigma _{\text{f}}} $的环形磁场时$ \theta = {135^ \circ } $的Kα辐射的对比度$ {C_{{{{\mathrm{K}}\alpha }}}} $ (a) $ {\sigma _{\text{f}}} = 20{\text{ μm}} $时$ {C_{{{{\mathrm{K}}\alpha }}}} $与$ {B_0} $的关系; (b) $ {B_0} = 100{\text{ T}} $时$ {C_{{{{\mathrm{K}}\alpha }}}} $与$ {\sigma _{\text{f}}} $的关系
Fig. 10. Contrasts of Kα emission at $ \theta = {135^ \circ } $ versus $ {B_0} $ and $ {\sigma _{\text{f}}} $ of annular magnetic fields: (a) The dependence of $ {C_{{{{\mathrm{K}}\alpha }}}} $ on $ {B_0} $ with $ {\sigma _{\text{f}}} = 20{\text{ μm}} $; (b) the dependence of $ {C_{{{{\mathrm{K}}\alpha }}}} $ on $ {\sigma _{\text{f}}} $ with $ {B_0} = 100{\text{ T}} $.
图 11 不同环形磁场下的电子轨迹
Fig. 11. Trajectories of electrons in different annular magnetic fields.
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