init commit

.github/workflows/ci-workflow.yml

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+# This is a basic workflow to help you get started with Actions
+
+name: CI
+
+# Controls when the action will run. Triggers the workflow on push or pull request
+# events but only for the main branch
+on:
+  push:
+    branches: [ main ]
+  pull_request:
+    branches: [ main ]
+
+# A workflow run is made up of one or more jobs that can run sequentially or in parallel
+jobs:
+  test:
+    runs-on: ${{ matrix.os }}
+    strategy:
+      fail-fast: false
+      matrix:
+        julia-version: ['1.7']
+        julia-arch: [x64]
+        os: [ubuntu-latest]
+
+    # Steps represent a sequence of tasks that will be executed as part of the job
+    steps:
+      # Checks-out your repository under $GITHUB_WORKSPACE, so your job can access it
+      - uses: actions/checkout@v2
+
+      - name: "Set up Julia"
+        uses: julia-actions/setup-julia@v1
+        with:
+          version: ${{ matrix.julia-version }}
+
+      - name: "Build package"
+        uses: julia-actions/julia-buildpkg@latest
+
+      - name: "Run tests"
+        uses: julia-actions/julia-runtest@latest
+
+      - name: "Process coverage report"
+        uses: julia-actions/julia-processcoverage@v1
+
+      - name: Upload coverage to Codecov
+        uses: codecov/codecov-action@v2
+        with:
+          file: ./lcov.info

.github/workflows/documentation.yml

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+name: Documentation
+
+on:
+  push:
+    branches:
+      - main
+    tags: '*'
+  pull_request:
+
+jobs:
+  build:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v2
+      - uses: julia-actions/setup-julia@latest
+        with:
+          version: '1.6'
+      - name: Install dependencies
+        run: julia --project=docs/ -e 'using Pkg; Pkg.develop(PackageSpec(path=pwd())); Pkg.instantiate()'
+      - name: Build and deploy
+        env:
+          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
+          DOCUMENTER_KEY: ${{ secrets.DOCUMENTER_KEY }}
+        run: julia --project=docs/ docs/make.jl
+

.gitignore

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+.DS_Store
+docs/derivation_notes.lyx~
+docs/#derivation_notes.lyx#
+docs/stringchanger.sh
+stringchanger.sh
+statprof
+profile.pb.gz
+derivation_*.txt
+*.pdf
+*.sh
+*.jld
+*.jld2

LICENSE

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+MIT License
+
+Copyright (c) 2018 J W S Cook
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

Project.toml

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+name = "LinearMaxwellVlasov"
+uuid = "b1137d70-0135-468f-bb3e-ace6f597c457"
+authors = ["James Cook <[email protected]>"]
+version = "0.1.0"
+
+[deps]
+CommonSubexpressions = "bbf7d656-a473-5ed7-a52c-81e309532950"
+DualNumbers = "fa6b7ba4-c1ee-5f82-b5fc-ecf0adba8f74"
+HCubature = "19dc6840-f33b-545b-b366-655c7e3ffd49"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+Memoize = "c03570c3-d221-55d1-a50c-7939bbd78826"
+MuladdMacro = "46d2c3a1-f734-5fdb-9937-b9b9aeba4221"
+QuadGK = "1fd47b50-473d-5c70-9696-f719f8f3bcdc"
+SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+
+[compat]
+CommonSubexpressions = "≥ 0.3"
+DualNumbers = "≥ 0.6.5"
+HCubature = "≥ 1.5.0"
+Memoize = "≥ 0.4.4"
+QuadGK = "≥ 2.4.1"
+SpecialFunctions = "≥ 1.5.1"
+StaticArrays = "≥ 1.2.7"
+
+[extras]
+Dates = "ade2ca70-3891-5945-98fb-dc099432e06a"
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
+Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+UnitTestDesign = "239896fa-e45a-40e8-9993-3c434b0bc450"
+
+[targets]
+test = ["Dates", "ForwardDiff", "InteractiveUtils", "Random", "Statistics", "Test", "UnitTestDesign"]

README.md

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+# LinearMaxwellVlasov.jl
+
+![CI](https://github.com/jwscook/LinearMaxwellVlasov.jl/workflows/CI/badge.svg)
+[![codecov.io](http://codecov.io/github/jwscook/LinearMaxwellVlasov.jl/coverage.svg?branch=main)](http://codecov.io/github/jwscook/LinearMaxwellVlasov.jl?branch=main)
+
+Solutions to the homogeneous linear Vlasov-Maxwell equations.
+
+This code solves for the dispersion relation of the linearised Maxwell-Vlasov equations for an infinite, spatially homogenous plasma. Multiple models of plasma species are available: 
+ 1. cold fluid
+ 1. warm fluid with optionally distinct parallel and perpendicular sound speeds
+ 1. kinetic (bi-)Maxwellian with optional parallel drift
+ 1. kinetic parallel Maxwellian with optional drift with "ring" perpendicular drift
+ 1. arbitrary decoupled parallel and perpendicular distribution functions. 
+ 1. relativistic species (not battle tested)
+
+It is possible to solve for complex wavenumbers indicative of convective instabilities.
+
+<img src="/misc/equations/LinearisedMaxwellValasov.png" height="50" />
+
+which is far to big to display here. The relationships between the species contribution and the dielectric tensor and perturbed current are
+
+<img src="/misc/equations/Relationship1.png" height="50" />
+<img src="/misc/equations/Relationship2.png" height="50" />
+
+References:
+
+Books: Stix, Melrose, Brambilla
+
+Particularly useful and succinct:
+Chapter 15, "Electromagnetic Waves in Plasma" by Takayuki Umeda, Nagoya University Japan in book "Wave Propagation", edited by Andrey Petrin, published March 16th 2011 by IntechOpen
+https://www.intechopen.com/books/wave-propagation

docs/Project.toml

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+[deps]
+Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
+
+[compat]
+Documenter = "0.27"
+

docs/make.jl

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+using Documenter, LinearMaxwellVlasov
+
+makedocs(sitename="LinearMaxwellVlasov.jl")
+
+deploydocs(
+    repo = "github.com/jwscook/LinearMaxwellVlasov.jl.git",
+)

docs/src/index.md

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+# LinearMaxwellVlasov.jl Documentation
+
+```@meta
+CurrentModule = LinearMaxwellVlasov
+```
+
+```@autodocs
+Modules = [LinearMaxwellVlasov]
+```
+
+## Index
+
+```@index
+```

examples/BumpOnTail.jl

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+using Dates
+
+println("Starting BumpOnTail at ", now())
+using LinearMaxwellVlasov
+using Random, Profile, StatProfilerHTML
+using Optim, Plots, LinearAlgebra, NelderMead
+using BenchmarkTools, InteractiveUtils
+Plots.gr()
+Random.seed!(0)
+
+function run()
+  mₑ = LinearMaxwellVlasov.mₑ
+  mi = 1836*mₑ
+  n0 = 1.0e19
+  Πe = plasmafrequency(n0, mₑ, -1)
+  Ωe = 1.0e-8 * Πe
+  ϵV = 1.0e2
+  vthe = thermalspeed(ϵV, mₑ)
+  vd = -6.0 * vthe
+  λD = vthe / Πe
+  kD = 2π/λD
+  ratio = 1.0e-3
+
+  fu(v)  = exp.(-v.^2/vthe^2) + ratio * exp.(-(v-vd).^2/vthe^2)
+  f_parallel = FParallelNumerical(fu, -10*vthe + vd, vd + 10*vthe)
+
+  electron_and_beam = SeparableVelocitySpecies(Πe, Ωe, f_parallel,
+      FPerpendicularNumerical(vthe))
+  Snum = Plasma([electron_and_beam])
+
+  electron_max = MaxwellianSpecies(Πe*sqrt(1.0-ratio), Ωe, vthe, vthe)
+  beam_max = MaxwellianSpecies(Πe*sqrt(ratio), Ωe, vthe, vthe, vd)
+  Smax = Plasma([electron_max, beam_max])
+
+  electron_rb = RingBeamSpecies(Πe*sqrt(1.0-ratio), Ωe, vthe, vthe)
+  beam_rb = RingBeamSpecies(Πe*sqrt(ratio), Ωe, vthe, vthe, vd)
+  Srb = Plasma([electron_rb, beam_rb])
+
+  plot_it = false
+  if plot_it
+    v = Vector(range(-12.0*vthe, stop=12.0*vthe, length=10000))
+    Plots.plot(v/(Πe/kD), electron_and_beam.Fb.F(v)/vthe, linestyle=:cyan)
+    Plots.plot!(v/(Πe/kD), electron_and_beam.Fb.dFdv(v), linestyle=:black)
+  end
+  function f!(C::Configuration, x::Vector{T}, S) where {T<:Number}
+    C.frequency = ComplexF64(x[1], x[2])
+    return abs(tensor(S, C)[3, 3])
+  end
+
+  N = 64
+  ks = Vector{Float64}(range(1.0e-3, stop=1.0, length=N)) .* 0.08
+  ks = sort(vcat(-ks, ks))
+  O = Options()
+  F = (1.05 + im * 0.1)*Πe
+  K = Wavenumber()
+  C = Configuration(F, K, O)
+
+  function solve(args)
+    solutions = Vector()
+    @show N, args[end]
+    for i ∈ eachindex(ks)
+      objective, config, lb, ub = args
+      c = deepcopy(config)
+      c.wavenumber = Wavenumber(wavenumber=ks[i] * kD,
+        propagationangle=1.0e-8*π)
+      neldermeadsol = NelderMead.optimise(x->norm(objective(c, x)),
+        (ub .+ lb) / 2, (ub .- lb) ./ 1000; stopval=1.0e-4, timelimit=10)
+      val, minimizer, returncode, numiterations = neldermeadsol
+      if returncode == :STOPVAL_REACHED
+        objective(c, minimizer)
+        push!(solutions, c)
+      end
+    end
+    return solutions
+  end
+  f!max(C, x) = f!(C, x, Smax)
+  f!rb(C, x) = f!(C, x, Srb)
+  f!num(C, x) = f!(C, x, Snum)
+  args = Vector{Any}()
+  push!(args, (f!max, C, [0.9, -0.1]*Πe, [1.5, 0.2]*Πe))
+  push!(args, (f!rb, C, [0.9, -0.1]*Πe, [1.5, 0.2]*Πe))
+  push!(args, (f!num, C, [0.9, -0.1]*Πe, [1.5, 0.2]*Πe))
+
+  @time for (arg, title) in zip(args, ("Maxwellian", "Ring-Beam", "Quadrature"))
+    @time solutions = solve(arg)
+    ω = [solution.frequency for solution in solutions]
+    Ks = [para(solution.wavenumber) for solution in solutions]
+
+    ωanalytical = sqrt.(Πe^2 .+ 3*(Ks*vthe).^2)
+    dFdv = f_parallel.(ωanalytical ./ Ks, true)
+    γanalytical = π/2 * ωanalytical * Πe.^2 ./ Ks.^2 .* sign.(Ks) .* dFdv
+
+    h = Plots.plot(Ks / kD, ωanalytical ./ Πe,
+                  markercolor=:blue, markershape=:circle,
+                  xlabel="\$Wavenumber [2\\pi / \\lambda_D]\$",
+                  ylabel="\$Frequency [\\Omega_{pe}]\$")
+    Plots.plot!(Ks / kD, γanalytical ./ Πe,
+               markercolor=:blue, markershape=:square)
+    Plots.scatter!(Ks / kD, real.(ω) ./ Πe,
+                  markercolor=:green, markershape=:circle)
+    Plots.scatter!(Ks / kD, imag.(ω) ./ Πe,
+                  markercolor=:green, markershape=:square)
+    Plots.plot!(legend=false)
+    Plots.savefig("$title.pdf")
+  end
+end
+run()
+println("Ending at ", now())