G01_MCC

模块定位

G01_MCC 是基于 null-collision 的 Monte Carlo Collision 模块。它读取碰撞截面表，用截面和粒子速度计算各类碰撞频率，随机选取本步需要测试的粒子，并按碰撞类型更新速度、生成电离二次粒子或累积电离源项。

文件角色
文件	角色
mod_G01_collision.f90	模块包装器，include G01 的截面读取、插值、电子碰撞和离子碰撞例程。
sub_G01_load_cross_section.f90	从两列文本文件读取能量-截面表，并把短表补到 `Nmax`。
fun_G01_cross_section.f90	对等间隔能量表做线性插值，超出表范围时使用边界截面。
sub_G01_collision1.f90	电子-中性粒子 MCC；支持弹性散射、激发和电离，并在电离时生成新电子/离子。
sub_G01_collision2.f90	离子-中性粒子 MCC；支持电荷交换和离子-中性粒子弹性散射。
sub_G01_electron.f90	电子碰撞后的散射角、能量损失和二次粒子速度抽样。

Null-Collision 流程

当前 G01_MCC 的 null-collision 选择流程、电子散射角抽样和散射角几何示意遵循 Vahedi 和 Surendra 的 MCC 算法文献。

为避免每个时间步对所有粒子逐个计算碰撞概率，MCC 先构造一个覆盖所有能量和位置的最大频率 nu_prime：

\[\nu' = \max_{x,E}\left(n_t(x)\,\sigma_T(E)\,v(E)\right) = \max_x n_t(x)\,\max_E\left(\sigma_T(E)v(E)\right)\]

时间步 dt 内被抽中进入碰撞测试的最大概率为

\[P_{\mathrm{null}} = 1 - \exp(-\nu' \Delta t)\]

例程用 P_null * np 得到本步测试粒子数 Nc，随机选取不重复粒子。对每个被选粒子，先根据当前位置插值得到中性粒子密度 n_t，再对每个碰撞类型计算

\[\nu_j(E_i) = n_t\,\sigma_j(E_i)\,v_i\]

随机数 R 落入累积区间 sum(nu_1..nu_j) / nu_prime 时执行第 j 类真实碰撞；若没有落入任何真实碰撞区间，则本次测试是 null collision，粒子状态保持不变。

已实现的碰撞类型

sub_G01_collision1 用 collision_type 区分电子碰撞：

1：电子-中性粒子弹性散射。
2：激发；电子损失 energy_excitation。
3：电离；电子损失 energy_ionization，产生一个新电子和一个新离子，并把源项沉积到 S。

sub_G01_collision2 用 collision_type 区分离子碰撞：

1：电荷交换，离子速度替换为抽样得到的中性粒子速度。
2：离子-中性粒子散射，使用各向同性方向抽样更新相对速度。

当前 Sphinx 页只按源码中已有路径说明实现状态。分子解离、解离电离和解离附着等过程可按相同 MCC 选择框架扩展，但当前 G01_MCC 源码没有对应分支。

电子散射角和能量损失

电子碰撞核使用 Vahedi 风格的角度抽样。入射电子能量为 energy 时，散射角满足

\[\cos\chi = \frac{2 + \epsilon - 2(1+\epsilon)^R}{\epsilon}\]

其中 R 是 [0,1] 上的随机数，epsilon 是按例程参数 eV 缩放后的能量。方位角 phi = 2 pi R' 均匀抽样。弹性碰撞的能量损失按

\[\Delta E = \frac{2m_e}{m_n}(1-\cos\chi)E\]

激发直接扣除激发阈值；电离把剩余能量在保留电子和新电子之间平均分配。

../../_images/G01_MCC_scatterangle.png — 电子碰撞散射角几何关系；图示来自 Vahedi 和 Surendra (1995)。

参考文献

V. Vahedi and M. Surendra, A Monte Carlo collision model for the particle-in-cell method: applications to argon and oxygen discharges, Computer Physics Communications 87 (1995) 179-198. DOI: 10.1016/0010-4655(94)00171-W.

调用注意

nu_max < 0 时例程会重新扫描截面表以初始化最大 sigma*v；后续调用可复用 nu_max。
den 和 S 使用 il(1)-1:iu(1) 等节点范围，粒子坐标需要落在可插值的网格单元内。
当前代码假设位置坐标已经按网格间距归一化，内部注释也指出 dx=dy=dz=1。
np1/np2 可能因电离增加；调用方需要保证 npmax1/npmax2 留有容量。
截面表的能量单位、粒子质量、电荷常数和 eV 换算需要由调用方保持一致。

Module Role

G01_MCC implements a null-collision Monte Carlo Collision layer. It loads tabulated collision cross sections, evaluates collision frequencies from cross sections and particle speed, samples particles that need collision tests in the current step, and then updates velocities, creates ionization products, or accumulates ionization source terms.

File Roles
File	Role
mod_G01_collision.f90	Module wrapper including the G01 table loader, interpolation helper, electron collision routine, and ion collision routine.
sub_G01_load_cross_section.f90	Load a two-column energy/cross-section table and extend short tables to `Nmax`.
fun_G01_cross_section.f90	Linearly interpolate a uniformly spaced energy table and clamp out-of-range energies to boundary values.
sub_G01_collision1.f90	Electron-neutral MCC for elastic scattering, excitation, and ionization, including secondary electron/ion creation.
sub_G01_collision2.f90	Ion-neutral MCC for charge exchange and ion-neutral elastic scattering.
sub_G01_electron.f90	Sample electron scattering angles, energy loss, and secondary-particle velocities.

Null-Collision Workflow

The current G01_MCC null-collision selection workflow, electron scattering-angle sampling, and scattering-angle geometry follow the MCC algorithm paper by Vahedi and Surendra.

To avoid testing every particle against every physical reaction in every time step, MCC first constructs a maximum frequency nu_prime that bounds all energies and positions:

\[\nu' = \max_{x,E}\left(n_t(x)\,\sigma_T(E)\,v(E)\right) = \max_x n_t(x)\,\max_E\left(\sigma_T(E)v(E)\right)\]

The maximum probability that a particle is selected for collision testing during one time step is

\[P_{\mathrm{null}} = 1 - \exp(-\nu' \Delta t)\]

The routines use P_null * np to obtain the number Nc of particles to test, then randomly select distinct particles. For each selected particle, the neutral density n_t is interpolated from the particle position, and each reaction frequency is evaluated as

\[\nu_j(E_i) = n_t\,\sigma_j(E_i)\,v_i\]

A random number R selects a physical reaction when it falls inside the cumulative interval sum(nu_1..nu_j) / nu_prime. If no physical interval is selected, the event is a null collision and the particle state is unchanged.

Implemented Collision Types

sub_G01_collision1 uses collision_type for electron collisions:

1: electron-neutral elastic scattering.
2: excitation; the electron loses energy_excitation.
3: ionization; the electron loses energy_ionization, a new electron and ion are created, and the source term is deposited into S.

sub_G01_collision2 uses collision_type for ion collisions:

1: charge exchange, replacing the ion velocity with a sampled neutral velocity.
2: ion-neutral scattering, updating the relative velocity with an isotropic direction sample.

This page documents the paths implemented in the current source. Molecular dissociation, dissociative ionization, and dissociative attachment can be added under the same MCC selection framework, but they do not have branches in the current G01_MCC routines.

Electron Scattering and Energy Loss

The electron kernel uses Vahedi-style angular sampling. For an incident electron energy energy, the scattering angle satisfies

\[\cos\chi = \frac{2 + \epsilon - 2(1+\epsilon)^R}{\epsilon}\]

where R is a uniform random number in [0,1] and epsilon is the energy scaled by the routine argument eV. The azimuthal angle phi = 2 pi R' is sampled uniformly. Elastic energy loss is

\[\Delta E = \frac{2m_e}{m_n}(1-\cos\chi)E\]

Excitation subtracts the excitation threshold directly. Ionization splits the remaining energy equally between the retained electron and the new electron.

Reference

V. Vahedi and M. Surendra, A Monte Carlo collision model for the particle-in-cell method: applications to argon and oxygen discharges, Computer Physics Communications 87 (1995) 179-198. DOI: 10.1016/0010-4655(94)00171-W.

Calling Notes

When nu_max < 0, the routine scans the cross-section tables to initialize the maximum sigma*v; later calls can reuse nu_max.
den and S use node ranges such as il(1)-1:iu(1). Particle positions must remain inside cells that can be interpolated from those nodes.
The current code assumes positions are normalized by the grid spacing; an internal comment notes dx=dy=dz=1.
np1 and np2 may increase after ionization, so callers must leave capacity in npmax1 and npmax2.
Cross-section energy units, particle masses, charge constants, and the eV conversion factor must be kept consistent by the caller.