testparticle.jl

### A Pluto.jl notebook ###
# v0.19.16

using Markdown
using InteractiveUtils

# ╔═╡ 179f8ca3-5adb-4e0c-8a02-fc94b02e4d48
begin
    using TestParticle
    using TestParticle: get_gc, getB_dipole, getE_dipole, sph2cart, Rₑ
    using TestParticleMakie
    using OrdinaryDiffEq
    using StaticArrays
    using LinearAlgebra
    using PlutoUI
end

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html"<button onclick='present()'>present</button>"

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TableOfContents()

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md"""
# 基于开源工具链的测试粒子模型

周弘扬，刘天成

Julia中文社区2022冬季见面会

2022年12月7日
"""

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md"""

## 什么是测试粒子？

测试粒子是一个**非自洽**的场-粒子作用模型。完整的粒子相空间轨迹描述不仅需要反映场对粒子的作用，也需要反映粒子对场的作用。

**场** <--> **粒子**

然而，作为近似处理，我们可以忽略少量粒子对场的反馈，而仅关注场对粒子的作用。

**场** --> **粒子**

$(Resource("https://www.schoolphysics.co.uk/age14-16/Electricity%20and%20magnetism/Current%20electricity/text/Particles_and_fields/images/2.png"))

## 测试粒子的意义

- 求解高中物理题


- 研究粒子在复杂外场中的行为


- 解释集体运动模式


- 代替昂贵的实验

$(Resource("https://raw.githubusercontent.com/henry2004y/TestParticlePresentation/master/single_trajectory_static_B.png"))
"""

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md"""

## 带电粒子运动

### 非相对论情况

```math
m\frac{\mathrm{d}\mathbf{v}}{\mathrm{d}t} = q(\mathbf{E} + \mathbf{v}\times\mathbf{B}) \tag{1}
```

### 相对论情况

满足洛伦茨协变的四维动量方程：

```math
\frac{\mathrm{d}p^\mu}{\mathrm{d}\tau} = \gamma qF^{\mu \nu}v_\nu \tag{2}
```

其中$\gamma = 1/\sqrt{1-v^2/c^2}$， $\tau$为固有时间， $p^\mu = \gamma m v^\mu$为四维动量，$F^{\mu\nu}$ 为电磁场张量。

简化后在三维空间中可写出两种计算中可用的形式：

 
```math
\frac{\mathrm{d}(\gamma v^i)}{\mathrm{d}t} = \frac{q}{m}(E^i+\epsilon^{ijk}v_j B_k) \tag{3}
```

或者

```math
\frac{\mathrm{d}v^i}{\mathrm{d}t} = \frac{q}{m \gamma^3}(E^i+\epsilon^{ijk}v_j B_k) \tag{4}
```

经测试， Eq.(3) 的数值计算精度要好于 Eq.(4)。
"""

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md"""

## Julia社区生态

1. `DifferentialEquations`是社区中开发最早，规模最大的包之一。其中，`OrdinaryDiffEq`是一个针对常微分方程的通用求解库。


2. `Interpolations`是社区中最常使用的高性能插值库，提供了针对不同网格、不同精度、不同算法的支持。


3. `StaticArrays`是社区中针对栈内存数组的优化库，提供了目前Julia本身不支持的对小体量定长数组的内存优化。


4. `Meshes`是一个近几年新开发的针对不同网格的底层支持库。


5. `SpecialFunctions`一个特殊数学函数的Julia原生实现。


6. `Makie`是一个面向GPU的新一代Julia原生绘图库。
"""

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md"""

## Julia开源社区的优势

- 积木式组合，避免造轮子
  - 个人能力有穷时
  - 利用庞大的开源算法库


- 语言层面的接口对接十分便捷
  - 泛型的支持
  - 性能的考虑


- 与陌生人合作

"""

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md"""
## TestParticle.jl目标

1. 简洁：用户只需提供场信息和粒子初始条件


2. 通用：适配一般模型，可独立运行


3. 高效：C的效率


4. 美观：对接强大的可视化工具
"""

# ╔═╡ 164d6f9c-98cd-44d3-b443-5ee0d7fb146b
md"""
## 设计

```julia
param = prepare(E, B, species)
prob = ODEProblem(trace!, stateinit, tspan, param)
sol = solve(prob, algorithm)
```

- 是否使用解析场？
- 是否有外场？
- 是否考虑时变？
- 是否考虑相对论？
- 是否使用原地替代（in-place）算法？

利用Julia的多重派发特性进行简化，归类为四个常微分函数(32 -> 4)

- `trace`
- `trace!`
- `trace_relativistic`
- `trace_relativistic!`
"""

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md"""
## 实现:是否时变？

- 否 --> 向`trace`传递场函数
- 是 --> 向`trace`传递含时场函数
  - 始终向场函数传入时间参数`t`❌
    - 简单，不优雅
  - 元编程❌
    - 作用域问题
    - 返回函数类型`#var...(typeof(E))`，在stacktrace中难以理解
```julia
function trace(y, p::TPTuple, t)
   q, m, E, B = p
   v = @view y[4:6]
   dx, dy, dz = v
   dux, duy, duz = q/m*(E(y, t) + v × (B(y, t)))
   SVector{6}(dx, dy, dz, dux, duy, duz)
end
```
```julia
function prepare(E, B; species::Species=Proton, q=1.0, m=1.0)
   q, m = getchargemass(species, q, m)
   name = nameof(E)
   E = @eval $name(xu, t) = $name(xu)
   # B ...

   q, m, E, B
end
```

## 实现:是否时变？（续）
  - 定义新类型`AbstractField`和`Field` ✅
  - 函数的类型稳定性

方法一：
```julia
abstract type AbstractField end

struct TimeDepedentField{F} <: AbstractField
   field_function::F
end

struct TimeIndepedentField{F} <: AbstractField
   field_function::F
end

(f::TimeDepedentField)(xu, t) = f.field_function(xu, t)
(f::TimeIndepedentField)(xu, t) = f.field_function(xu)

Field(B) = is_time_dependent(B) ? TimeDepedentField(B) : TimeIndepedentField(B)
```
方法二：
```julia
abstract type AbstractField{itd} end

struct Field{itd, F} <: AbstractField{itd}
   field_function::F
end

Field(f::Function) = Field{is_time_dependent(f), typeof(f)}(f)

(f::AbstractField{true})(xu, t) = f.field_function(xu, t)
(f::AbstractField{true})(xu) = error("...")
(f::AbstractField{false})(xu, t) = f.field_function(xu)
(f::AbstractField{false})(xu) = f.field_function(xu)
```

## 实现:是否解析？

- 是 --> `Field(F)`
- 否 --> 数值场，需要插值
```julia
function getinterp(A, gridx, gridy, gridz)
   Ax = @view A[1,:,:,:]
   itp = extrapolate(interpolate(Ax, BSpline(Cubic(Line(OnGrid())))), NaN)
   interpx = scale(itp, gridx, gridy, gridz)

   # ...

   # Return field value at a given location.
   function get_field(xu)
      r = @view xu[1:3]

      return SA[interpx(r...), interpy(r...), interpz(r...)]
   end

   return Field(get_field)
end
```

## 实现:可视化

- `Plot`： `DifferentialEquations`有原生支持


- `PyPlot`：无原生支持，需要额外的获取轨迹的代码


- `Makie`：Julia原生绘图库
  - 初步的plotting recipes支持
    - `MakieCore`仅支持plotting对象,不支持Figure, Axis对象
    - `Makie`本身较大的依赖
  - 独立的绘图支持库TestParticleMakie
    - 避免了`Requires.jl`带来的预编译问题
    - 借鉴了`DynamicalSystems.jl`的设计
"""

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md"""
## 展示：原始数据
"""

# ╔═╡ 39135c86-8585-43a3-acd6-42f012aac65b
begin
	# Magnetic field
	B(x) = SA[0, 0, 1e-8]
	# Electric field
	E(x) = SA[0, 0, 0]
	# Initial conditions
	x0 = [1.0, 0.0, 0.0]
	v0 = [0.0, 1.0, 0.1]
	stateinit = [x0..., v0...]
	tspan = (0, 20)
	# Assemble particle + fields
	param = prepare(E, B, species=Proton)
	prob = ODEProblem(trace!, stateinit, tspan, param)
	# Trace trajectory and save positions & velocities
	sol = solve(prob, Tsit5(); save_idxs=[1,2,3,4,5,6])
end

# ╔═╡ 56ee3992-c701-41bc-a5df-679a76ec3e48
md"""
## 展示：电子和质子运动
$(Resource("https://raw.githubusercontent.com/henry2004y/TestParticlePresentation/master/double_trajectories_static_B.png"))
"""

# ╔═╡ b02ac7ae-0bde-4606-8478-6a31f40d88f6
md"""
## 展示：绝热运动
$(Resource("https://raw.githubusercontent.com/henry2004y/TestParticlePresentation/master/adiabatic_trajectory_dipole.png"))
"""

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md"""
## 展示：磁层粒子运动
- 多粒子体系
  - `EnsembleProblem`内存开销问题
  - 额外的并行方法

$(Resource("https://raw.githubusercontent.com/henry2004y/TestParticlePresentation/master/electron_fixedtime_pm0.5RE_EGI_t1298.mp4", :autoplay => "", :loop => ""))
"""

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md"""
## 总结与展望
- `TestParticle.jl`可以作为简单的针对特定问题的求解器样本。


- 社区提供的强大支持使得程序开发周期大幅缩短。


- 计算及可视化技术的进步对于物理理解多有裨益。

#### 下一步：
- 多粒子体系采样
- 大规模并行测试
"""

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[[deps.TriangularSolve]]
deps = ["CloseOpenIntervals", "IfElse", "LayoutPointers", "LinearAlgebra", "LoopVectorization", "Polyester", "SnoopPrecompile", "Static", "VectorizationBase"]
git-tree-sha1 = "9126e77b5d1afee9f94e8a66165e3716603d6054"
uuid = "d5829a12-d9aa-46ab-831f-fb7c9ab06edf"
version = "0.1.15"

[[deps.Tricks]]
git-tree-sha1 = "6bac775f2d42a611cdfcd1fb217ee719630c4175"
uuid = "410a4b4d-49e4-4fbc-ab6d-cb71b17b3775"
version = "0.1.6"

[[deps.TriplotBase]]
git-tree-sha1 = "4d4ed7f294cda19382ff7de4c137d24d16adc89b"
uuid = "981d1d27-644d-49a2-9326-4793e63143c3"
version = "0.1.0"

[[deps.URIs]]
git-tree-sha1 = "ac00576f90d8a259f2c9d823e91d1de3fd44d348"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.4.1"

[[deps.UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[deps.UnPack]]
git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b"
uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
version = "1.0.2"

[[deps.Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

[[deps.UnicodeFun]]
deps = ["REPL"]
git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
version = "0.4.1"

[[deps.VectorizationBase]]
deps = ["ArrayInterface", "CPUSummary", "HostCPUFeatures", "IfElse", "LayoutPointers", "Libdl", "LinearAlgebra", "SIMDTypes", "Static"]
git-tree-sha1 = "fc79d0f926592ecaeaee164f6a4ca81b51115c3b"
uuid = "3d5dd08c-fd9d-11e8-17fa-ed2836048c2f"
version = "0.21.56"

[[deps.VertexSafeGraphs]]
deps = ["Graphs"]
git-tree-sha1 = "8351f8d73d7e880bfc042a8b6922684ebeafb35c"
uuid = "19fa3120-7c27-5ec5-8db8-b0b0aa330d6f"
version = "0.2.0"

[[deps.WoodburyMatrices]]
deps = ["LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "de67fa59e33ad156a590055375a30b23c40299d3"
uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
version = "0.5.5"

[[deps.XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "58443b63fb7e465a8a7210828c91c08b92132dff"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.9.14+0"

[[deps.XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.34+0"

[[deps.Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.6.9+4"

[[deps.Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.9+4"

[[deps.Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.3+4"

[[deps.Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.4+4"

[[deps.Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.10+4"

[[deps.Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.0+3"

[[deps.Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.13.0+3"

[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.4.0+3"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.12+3"

[[deps.ZygoteRules]]
deps = ["MacroTools"]
git-tree-sha1 = "8c1a8e4dfacb1fd631745552c8db35d0deb09ea0"
uuid = "700de1a5-db45-46bc-99cf-38207098b444"
version = "0.2.2"

[[deps.isoband_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "51b5eeb3f98367157a7a12a1fb0aa5328946c03c"
uuid = "9a68df92-36a6-505f-a73e-abb412b6bfb4"
version = "0.2.3+0"

[[deps.libaom_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4"
uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
version = "3.4.0+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl", "OpenBLAS_jll"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.1.1+0"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"

[[deps.libsixel_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Pkg", "libpng_jll"]
git-tree-sha1 = "d4f63314c8aa1e48cd22aa0c17ed76cd1ae48c3c"
uuid = "075b6546-f08a-558a-be8f-8157d0f608a5"
version = "1.10.3+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+1"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.48.0+0"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+0"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"
"""

# ╔═╡ Cell order:
# ╟─e53ae15f-5ad8-4e36-9a20-f9e74a24747a
# ╟─179f8ca3-5adb-4e0c-8a02-fc94b02e4d48
# ╟─bd3af018-1bf2-4200-84bd-35f596b723ce
# ╟─5791598a-6fbb-11ed-3f03-e7f48288a468
# ╟─5f976621-9acd-474a-a836-74f502274754
# ╟─4bf7aa87-d070-4389-8670-090a99100370
# ╟─bbcae7e7-2bdb-4a9c-8137-0c64cbc533b1
# ╟─dc580613-f43c-4047-9e2a-aa55d6ac113f
# ╟─91c29b75-62e3-44bc-a67a-c2d57ab1b059
# ╟─164d6f9c-98cd-44d3-b443-5ee0d7fb146b
# ╟─4c3be683-1d11-42d1-916c-b8318c0ecf3f
# ╟─3fa20598-d32e-40b6-98e9-06496027c646
# ╟─39135c86-8585-43a3-acd6-42f012aac65b
# ╟─56ee3992-c701-41bc-a5df-679a76ec3e48
# ╟─b02ac7ae-0bde-4606-8478-6a31f40d88f6
# ╟─fec5ab30-22a4-4726-9b05-eda55b290b66
# ╟─f3b73120-5e71-496f-8e6b-cac7be04bcf5
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002