Fund Project:Project supported by the National Natural Science Foundation of China (Grant No. 11805281)
Received Date:07 October 2019
Accepted Date:18 November 2019
Published Online:05 February 2020
Abstract:In order to improve the efficiency of the single event effect (SEE) experiments on the 100 MeV proton cyclotron of China Institute of Atomic Energy, a binary energy degrader that can lower the initial proton energy to other values rapidly is designed for the 100 MeV protons provided by the accelerator. The energy degrader is comprised of six aluminum plates of 0.5, 1, 2, 4, 8, 16 and 32 mm at thickness, where the thickness of the latter plate is twice that of the previous one. We introduce the concept of relative thickness, which can also represent the order of the energy of the produced protons, and the state or operation of the degrader. The energy interval of 61 protons with energy above 9.69 MeV, produced by the degrader, is between 0.84 MeV and 4.09 MeV. And their energy straggling degree is less than 10%, and full width at half maximum of the scattering angle is less than 45 mrad. So the energy degrader basically meets the requirements of the proton SEE experiments. The influence of the initial proton energy accuracy of the protons directly provided by the accelerator on the residual energy after they have passed through the degrader is discussed. It is found that the lower the residual energy, the greater the influence is. In addition, the degrader is also suitable for protons in the 70-100 MeV energy range that the accelerator can directly provide, and more continuous energy can be obtained by using more plates designed with this method. The design method of the energy reducer proposed in this paper is simple and effective, and has a strong reference value. Keywords:energy degrader/ single event effects/ energy straggling/ angle straggling
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3.1.降能效果
要计算穿过降能器之后质子的能量, 需要知道质子在铝中的能量-射程关系, 见图1. 能量为E、在铝中射程为R的质子, 在经过总厚度为ti的降能片组合之后, 其剩余能量记为Ei, 则Ei对应的在铝中的射程应为$ {R-{{t_{\rm{i}}}}} $, 从而Ei可由能量-射程关系通过插值的方法得到. 据此, 可以得到90.07 MeV的质子穿过64种不同降能片组合之后的能量, 如图2所示. 本文中涉及的能量-射程关系均由SRIM程序计算, SRIM是计算离子在物质中的阻止本领(–dE/dx)和射程的常用程序, 其关于质子在物质中的阻止本领(与射程密切相关)的计算值与将近9000个实验数据点的误差总体而言在3.9%以内[11,12], 足以保证上述能量-射程关系的准确性, 进而可保证计算的质子通过降能片之后的能量的准确性. 图 1 采用SRIM计算得到的1?100 MeV质子在铝中的阻止本领及射程 Figure1. Stopping power and range of 1?100 MeV protons in aluminum calculated by SRIM.
图 2 入射质子穿过64种不同降能片组合之后的能量 Figure2. Residual energies of the incident protons after they pass through the energy degrader with 64 kinds of combinations of 6 energy degrader plates.
$f\left( r \right) = \frac{1}{{{\text{π}}{R^2}}}\exp \left( { - \frac{{{r^2}}}{{{R^2}}}} \right),$
其中, $R = \sqrt 2 L{\theta _{{\rm{FWHM}}}}$, r为测量平面上任一位置到束流中心的距离. 由(3)式可见, 束流在经靶物质散射后, 除了产生角度岐离外, 还在横向方向上产生一定的扩展, 也使得粒子注量率产生一定程度的降低. 要详细了解进行质子SEE实验时DUT (device under test)位置处的束流横向分布情况, 需对质子SEE实验装置中的双散射靶、降能器、DUT以及所涉及的空间几何关系进行全面考虑. 为方便起见, 本文仅考虑降能器的影响, 且忽略各降能片之间实际存在的间隙, 在此情况下对质子束流在降能器中产生的角度岐离进行粗略的估计, 图4给出了通过(2)式计算得到的经降能器产生的各能点质子的角度歧离情况. 当tR = 61时, 质子剩余能量为3.21 MeV, 此时质子角度岐离最大, ${\theta _{{\rm{FWHM}}}}$为45.20 mrad. 降能器与DUT距离L约为0.25 m, 相应的$R = \sqrt 2 L{\theta _{{\rm{FWHM}}}} = 1.60$ cm, 即在DUT位置距离束流中心1.60 cm处质子注量率是束流中心处的$1 / {{\rm{e}}} \approx 36.79\% $. 在实际情况中, 各降能片之间的间隙及降能器前后存在的空气会使得角度歧离略微增大; 双散射靶也会导致质子束流产生角度歧离, 其位置距离DUT较远, 主要作用是对质子束流进行横向扩展, 使其均匀化[10]. 图 4 经过降能器产生的各能点质子的散射角半高宽 Figure4. Full width at half maximum of the scattering angle of the resulting protons at each energy point produced by the energy degrader.
23.4.初始质子能量精度的影响 -->
3.4.初始质子能量精度的影响
加速器直接引出的初始质子能量可能存在一定偏差, 假定引出100 MeV质子时偏差为0.1%, 探讨此时质子经降能器不同状态后剩余能量Ei的变化, 结果见图5. 可见, 质子经过降能器后的能量越低其偏差就越大. 以加速器引出100.1 MeV质子为例, 与引出100 MeV质子情况相比, 当tR = 1时, 经过降能器之后质子能量Ei由89.22 MeV提高0.11 MeV, 即0.12%; 当tR= 61时, Ei由3.21 MeV提高1.23 MeV, 即38.35%. 造成这种结果的原因是质子的阻止本领随着能量的降低而增高(见图1), 因此对同样厚度的铝而言, 质子能量越低, 在其中所损失的能量就越大. 如100 MeV质子在64.5 μm厚的铝内损失能量约为0.1 MeV, 而2.62 MeV的质子恰好在其中损失全部能量. 也正是由于同样的原因, 99.9 MeV情况造成的质子能量偏差要稍大于100.1 MeV情况. 类似地, 可以推测, Ei的能量越低, 铝片的加工精度、SRIM计算结果的精度给其带来的误差也就越大. 图 5 加速器直接提供的质子能量偏差0.1 MeV时造成质子经过降能器后剩余能量的偏差情况 Figure5. Variation of the residual energy after the protons with the energy deviation of 0.1 MeV directly provided by the accelerator pass through the energy degrader.
23.5.对70—100 MeV质子的适用性 -->
3.5.对70—100 MeV质子的适用性
加速器可直接提供70—100 MeV的质子, 故对所设计的降能器对其提供100, 90, 80, 70 MeV四种能量质子情况下的降能效果进行了考察. 双散射靶的存在使得四种情况下的质子能量分别降为90.07, 79.12, 68.15, 56.70 MeV, 使用降能器可提供的质子的最低能量分别为3.21, 6.75, 4.59, 8.29 MeV, 提供的各质子能点的最大间隔分别为6.48, 4.92, 5.78, 4.44 MeV, 在降能器状态tR分别为62, 49, 38, 27时即可将质子全部阻止, 如图6所示. 可见, 该降能器不仅适用于100 MeV质子, 对于加速器直接提供的70—100 MeV范围内的质子也都是基本适用的. 另外, 使用能量低的质子比使用能量高的质子经降能器降到同样的能量时所使用的降能片的总厚度小, 显然产生的能量岐离和角度岐离也小. 如100 MeV质子在tR = 40时能量降为49.58 MeV, 表征能量岐离的均方差参数σ为0.75 MeV, 散射角半高全宽${\theta _{{\rm{FWHM}}}}$为35.82 mrad; 而70 MeV质子在tR = 6时即降为49.21 MeV, 相应的σ仅为0.47 MeV, ${\theta _{{\rm{FWHM}}}}$仅为19.55 mrad. 图 6 降能器对加速器直接提供的100, 90, 80, 70 MeV 四种能量质子的降能效果 Figure6. Effects of the energy degrader for the protons at 100, 90, 80 and 70 MeV directly provided by the accelerator.