负二项分布随机变量数字特征的求解

本文给出了生产实践中被广泛应用的负二项分布的五种定义,研究了该分布对应随机变量的期望、方差等数字特征的求解,汇总了负二项分布与其它分布之间的关系.     

APTR质子同步加速器RFQ直线注入器的优化设计

为实现质子治疗装置的国产化和小型化,基于已完成安装调试的上海先进质子治疗装置(APTR),开展质子治疗注入器系统的升级设计研究,利用PARMTEQM设计软件和快聚束策略,针对APTR同步加速器RFQ直线注入器进行动力学设计模拟。RFQ工作频率为325 MHz,流强18 mA,对从离子源引出的低能质子束流进行匹配俘获、横向聚焦、纵向聚束和预加速,引出能量为3.0 MeV。通过优化预注入器RFQ动力学设计方案和极头参数,有效避免参数共振,减小束流损失,使其整体传输效率达到98.0%,在水平和垂直方向上的发射度增长分别为1.2%和3.3%,出口束流满足下一级腔体的注入需求,开展设计模拟验证和相关冗余度分析,为质子同步加速器的治疗设备和直线注入系统提供参照依据。     

IH型漂移管直线加速器的束流动力学研究（英文）

为了提高兰州重离子加速器冷却储存环（HIRFL-CSR）的运行效率、改善加速器输出束流品质,并实现几个加速装置分时供束,提高整个重离子加速装置的利用率,特为（HIRFL-CSR）增建一台新的注入器--CSRLINAC。在108.48 MHz的RFQ之后的CSR-LINAC主加速段,主要由一台108.48 MHz和两台216.96 MHz的IH型漂移管直线加速器组成,用于加速荷质比为1/8.5~1/3之间的重离子,其最大的束流流强为3 mA,并将粒子从0.3 MeV/u加速到3.71 MeV/u。运用KONUS动力学原理,在满足设计指标的情况下,首先利用TraceWin程序进行中能束线MEBT设计,后针对高频腔体设计和束流匹配的基本参数的系列讨论,特别是对CSR-LINAC的中能束流匹配线、参数选择和IH型KONUS结构的漂移管直线加速器进行设计模拟优化。最终得出,在保证腔体设计指标和95.3%的传输效率的情况下,该紧凑型直线加速结构经过三个腔体的加速后,束流的纵向归一化均方根发射度增长仅有25%;同时发现,当流强达到3 mA时,存在空间电荷效应,导致其纵向相宽增长约25%,最大横向包络也存在16.5%的涨落。In order to improve the operation efficiency of the Cooling Storage Ring of Heavy Ion Research Facility in Lanzhou (HIRFL-CSR), a heavy ion linac (linear accelerator) was proposed and designed as a new injector for HIRFL-CSR. Following the 108.48 MHz Radio-Frequency Quadrupole (RFQ), three tanks in total with Interdigital H-mode drift tube linac (IH-DTL) structure are installed to boost the beam energy from 0.3 to 3.71 MeV/u, and the beam current of ions with charge-to-mass ratio from 1/8.5 to 1/3 can reach to 3 mA. The first tank operatesat the same frequency as the RFQ, and the rest two operate at 216.96 MHz. The “Combined Zero-Degree Synchronous Particle Structure” (KONUS) beam dynamics was used in the beam dynamics design. The overview of the physics design on the main accelerating components, including RF design and beam dynamics design are introduced in this paper. The optimized structure design, fabrication status and simulation results are presented in this contribution. It shows that under the condition of assurance of 95.3% transmission efficiency, the normalized rms emittance is about 25%. When the beam current is up to 3 mA, owing to the space charge effect, the increase of longitudinal phase spread and transverse envelope are about 25% and 16.3%, respectively.     

基于特征函数的逆高斯分布统计性质研究

本文给出了基于特征函数的逆高斯分布众多统计性质的证明过程,对逆高斯分布与高斯分布的平行性质进行了归纳,对其应用特性进行了论述.     

时间序列分析中几个概念的解析

在时间序列分析的授课过程中，有一些概念性问题经常被学生所问及.本文对这些问题进行了汇总并给出了详细的解析.     

CSR-LINAC IH-RFQ的高频电磁设计

中国科学院近代物理研究所在CSR-LINAC项目中设计了一台108.48 MHz的IH型RFQ直线加速器。该RFQ可以将质荷比为3~7的离子从4 keV/u加速到300 keV/u。在完成束流动力学设计的基础上,主要针对RFQ腔体的高频电磁设计展开了研究,同时利用了电磁场仿真和束流动力学模拟来研究腔体的四极场不平整度和二极场及其动力学影响。未经调谐的情况下,腔体的谐振频率为108.15 MHz,腔体空载品质因子Q₀为5 910,腔体功耗为123 kW。通过在支撑板两端增加底切的设计,将腔体的四极场不平整度由-21%~ 12%优化至±2.5%,满足了束流动力学要求。腔体的二极场为-3%~ -2.2%,使得束流在垂直方向小幅振荡,RFQ的垂直方向接受度减小5%。为了保证功率馈入时反射较小,将耦合器设置在临界耦合状态,耦合面积为940 mm2。为了补偿腔体的频率偏差和漂移,设计了调谐量分别为707和132 kHz的固定调谐器和可动调谐器。The 108.48 MHz IH type RFQ for CSR-LINAC project is under design at Institute of Modern Physics, Chinese Academy of Sciences. This RFQ can accelerate heavy ions with mass to charge ratio of 3~7 from 4 keV/u to 300 keV/u. According to the beam dynamics requirement, the RF structure design has been finished. The quadrupole field unflatness and dipole field of the cavity were studied by electromagnetic simulation and beam dynamics simulation. The frequency of the cavity without tuning is 108.15 MHz, the Q₀ of the cavity is 5910, and the RF power loss is 123 kW. The quadrupole field unflatness of ±2.5%,which was -21%~12% before optimizing, is achieved to meet dynamics requirement through the undercuts in cavity supporters. The dipole field of -3%~ -2.2% causes the oscillation of the beam center and acceptance reduction of 5%. The power coupler must be in critical coupling state with the coupling area of 940 mm2 for minimum reflection coefficient. The tuners, consist of coarse and fine tuners with frequency shift of 707 and 132 kHz respectively, is used for tuning of frequency deviation of the cavity.     

HIRFL-CSRm冷却束流寿命

实验研究了HIRFL-CSRm中电子冷却装置对C6+,Ar15+两种束流寿命的影响。首先,通过对比实验的测量确定电子冷却可以有效提高束流寿命;其次,探究了电子冷却装置中的各项参数（主要是电子束密度分布、流强、能量、绝热展开因子）是如何影响束流寿命的,通过改变电子束参数,测量束流寿命的变化趋势和规律,并且结合电子冷却相关理论对实验结果给予解释,最终通过实验优化和确定最佳的冷却装置参数,使束流在HIRFL-CSRm上获得了较高的寿命,从而提高HIRFL-CSRm束流累积过程中的流强增益。     

Dirichlet分布统计性质汇总

Dirichlet分布是一种重要的多维连续概率分布族,广泛应用于贝叶斯统计,是成分数据和比例数据建模中变量分布类型的自然选择．本文对其所具有的优良统计性质进行了汇总证明．