Specificy the conductivity tensor (#6)

* properly specificy the conductivity tensor

* typo

* bump semver

Project.toml

@@ -1,7 +1,7 @@
 name = "LinearMaxwellVlasov"
 uuid = "b1137d70-0135-468f-bb3e-ace6f597c457"
 authors = ["James Cook <[email protected]>"]
-version = "0.1.4"
+version = "0.1.5"
 
 [deps]
 CommonSubexpressions = "bbf7d656-a473-5ed7-a52c-81e309532950"

src/LinearMaxwellVlasov.jl

@@ -49,7 +49,7 @@ export Cache
 # Plasmas
 export Plasma, NeutralPlasma, isneutral
 # Tensors
-export tensor, dielectric, electrostaticdielectric
+export tensor, dielectric, electrostatictensor, conductivity
 
 __precompile__(true) # precompile dependencies
 # precompile for species types

src/Tensors.jl

@@ -156,19 +156,28 @@ function contribution(species::AbstractKineticSpecies, config::Configuration,
 end
 
 """
-The dielectric tensor for a given species
+The contribution to the dielectric tensor for a given species
 """
-function dielectric(species::AbstractSpecies, config::Configuration,
+function dielectriccontribution(species::AbstractSpecies, config::Configuration,
     cache::Cache=Cache())
   return contribution(species, config, cache) * (species.Π / config.frequency)^2
 end
 
+"""
+The conducivity tensor for a given species
+"""
+function conductivity(species::AbstractSpecies, config::Configuration,
+    cache::Cache=Cache())
+  ϵᵢⱼₛ = dielectriccontribution(species, config, cache)
+  return -im * config.frequency * ϵ₀ * ϵᵢⱼₛ
+end
+
 """
 The dielectric tensor for a given plasma
 """
 function dielectric(plasma::AbstractPlasma, config::Configuration,
     cache::Cache=Cache())
-  ϵᵢⱼₛ = species -> dielectric(species, config, cache)
+  ϵᵢⱼₛ = species -> dielectriccontribution(species, config, cache)
   return mapreduce(ϵᵢⱼₛ, +, plasma) + I
 end
 
@@ -184,10 +193,12 @@ function tensor(plasma::AbstractPlasma, config::Configuration,
 end
 
 """
-The electrostatic dielectric tensor for a given plasma
+The electrostatic dielectric tensor for a given plasma, a zero valued
+determinant of which represents a solution to the linear
+poisson-vlasov system of equations
 """
-function electrostaticdielectric(plasma::AbstractPlasma, config::Configuration,
+function electrostatictensor(plasma::AbstractPlasma, config::Configuration,
     cache::Cache=Cache())
-  ϵₛ = s -> parallel(s, config, 0, UInt64(1), true) * s.Π^2 / config.frequency
-  return mapreduce(ϵₛ, +, plasma) + 1
+  return dielectric(plasma, config, cache)
 end
+

test/tensors/AnalyticalVsNumerical.jl

@@ -49,8 +49,8 @@ const LMV = LinearMaxwellVlasov
 #      ζ = kz * vthi / ω
       F = ComplexF64(ω, γ)
       C = Configuration(F, K, O)
-      time_a += @elapsed (ta = dielectric(M, C))
-      time_n += @elapsed (tn = dielectric(S, C))
+      time_a += @elapsed (ta = conductivity(M, C))
+      time_n += @elapsed (tn = conductivity(S, C))
       @test all(isapprox.(tn, ta, rtol=rtol, atol=atol))
       for i in 1:3, j in 1:3
         if !isapprox(tn[i, j], ta[i, j], rtol=rtol, atol=atol)
@@ -67,10 +67,10 @@ const LMV = LinearMaxwellVlasov
     C = Configuration(F, K)
     for Q ∈ (M, S)
       try
-        @inferred dielectric(Q, C)
+        @inferred conductivity(Q, C)
         @test true
       catch
-        @warn "dielectric not inferred for $(nameof(typeof(Q)))"
+        @warn "conductivity not inferred for $(nameof(typeof(Q)))"
         @test_broken false
       end
     end

test/tensors/Basic.jl

@@ -67,7 +67,7 @@ function performtest()
     K = Wavenumber(k=k, θ=0)
     C = Configuration((1.1 + 0.1*im)* Πe, K)
     output_tensor = tensor(S_num, C)[3,3]
-    output = electrostaticdielectric(S_num, C)
+    output = electrostatictensor(S_num, C)[3, 3]
     @test output_tensor ≈ output
   end
 
@@ -83,7 +83,7 @@ function performtest()
     config = Configuration(0 + im * Πe / 2,
                            Wavenumber(k=√3/2 * Πe / vbeam, θ=0.0))
     @test tensor(Plasma([left, right]), config)[3,3] ≈ 0 atol=eps()
-    @test electrostaticdielectric(Plasma([left, right]), config) ≈ 0 atol=eps()
+    @test electrostatictensor(Plasma([left, right]), config)[3, 3] ≈ 0 atol=eps()
   end
 end
 performtest()

test/tensors/ColdLimit.jl

@@ -7,7 +7,7 @@ using LinearMaxwellVlasov
 const LMV = LinearMaxwellVlasov
 
 
-@testset "Cold Limit Dielectrics" begin
+@testset "Cold Limit conductivities" begin
 
 mₑ = LMV.mₑ
 mi = 1836*mₑ
@@ -44,13 +44,13 @@ C = Configuration(F, K, O)
 
 tol = 1.0e-3
 
-outputCold = dielectric(cold, C)
-outputDelta = dielectric(delta, C)
-outputWarm = dielectric(warm, C)
-outputMaxwellian = dielectric(maxwellian, C)
-outputNumerical = dielectric(numerical, C)
-outputCoupled = dielectric(coupled, C)
-outputRelativistic = dielectric(relativistic, C)
+outputCold = conductivity(cold, C)
+outputDelta = conductivity(delta, C)
+outputWarm = conductivity(warm, C)
+outputMaxwellian = conductivity(maxwellian, C)
+outputNumerical = conductivity(numerical, C)
+outputCoupled = conductivity(coupled, C)
+outputRelativistic = conductivity(relativistic, C)
 for i ∈ 1:3, j ∈ 1:3
   expected = outputCold[i, j]
   @test expected ≈ outputDelta[i, j] rtol=tol atol=tol

test/tensors/CoupledVsSeparable.jl

@@ -40,7 +40,7 @@ Random.seed!(0)
       for params ∈ zip(σs, kzs)
         (σ, kz) = params
         F = ComplexF64(ωr, σ * ωr / 100)
-        K = Wavenumber(kz=k, k⊥=abs(k))
+        K = Wavenumber(kz=kz, k⊥=abs(k))
         iszero(K) && continue
         config = Configuration(F, K)
         config.options = Options(quadrature_rtol=1.0e-9, summation_rtol=1e-8)

test/tensors/NegativeKPara.jl

@@ -42,9 +42,9 @@ const LMV = LinearMaxwellVlasov
   end
 
   @testset "tensors" begin
-    outputM = dielectric(unitM, C)
-    outputN = dielectric(unitN, C)
-    outputR = dielectric(unitR, C)
+    outputM = conductivity(unitM, C)
+    outputN = conductivity(unitN, C)
+    outputR = conductivity(unitR, C)
     for i ∈ 1:9
       @test real(outputN[i]) ≈ real(outputM[i]) rtol=1.0e-6
       @test imag(outputN[i]) ≈ imag(outputM[i]) rtol=1.0e-6

test/tensors/RingBeamsAndPancakes.jl

@@ -40,12 +40,6 @@ const LMV = LinearMaxwellVlasov
 
   O = Options()
 
-  function f2Dω!(x::Vector{T}, C::Configuration, S, cache) where {T<:Number}
-    C.frequency = ComplexF64(x[1], x[2])
-    t = @elapsed output = det(dielectric(S, C, cache))
-    return output
-  end
-
   ks_positive = range(0.1, stop=100.0, length=2^3) * k0
   ks = sort(vcat(-ks_positive, ks_positive))
 
@@ -64,12 +58,12 @@ const LMV = LinearMaxwellVlasov
     C = Configuration(F, K, O)
     push!(configurations, C)
 
-    push!(vals_numerical_rb, dielectric(numerical_rb, C))
-    push!(vals_ringbeam_rb, dielectric(ringbeam_rb, C))
+    push!(vals_numerical_rb, conductivity(numerical_rb, C))
+    push!(vals_ringbeam_rb, conductivity(ringbeam_rb, C))
 
-    push!(vals_maxwellian_bp, dielectric(maxwellian_bp, C))
-    push!(vals_numerical_bp, dielectric(numerical_bp, C))
-    push!(vals_ringbeam_bp, dielectric(ringbeam_bp, C))
+    push!(vals_maxwellian_bp, conductivity(maxwellian_bp, C))
+    push!(vals_numerical_bp, conductivity(numerical_bp, C))
+    push!(vals_ringbeam_bp, conductivity(ringbeam_bp, C))
   end
 
   # these ones are different
@@ -81,30 +75,30 @@ const LMV = LinearMaxwellVlasov
     C = Configuration(F, K, O)
     push!(configurations, C)
 
-    push!(vals_numerical_rb, dielectric(numerical_rb, C))
-    push!(vals_ringbeam_rb, dielectric(ringbeam_rb, C))
+    push!(vals_numerical_rb, conductivity(numerical_rb, C))
+    push!(vals_ringbeam_rb, conductivity(ringbeam_rb, C))
 
-    push!(vals_maxwellian_bp, dielectric(maxwellian_bp, C))
-    push!(vals_numerical_bp, dielectric(numerical_bp, C))
-    push!(vals_ringbeam_bp, dielectric(ringbeam_bp, C))
+    push!(vals_maxwellian_bp, conductivity(maxwellian_bp, C))
+    push!(vals_numerical_bp, conductivity(numerical_bp, C))
+    push!(vals_ringbeam_bp, conductivity(ringbeam_bp, C))
   end
 
   @testset "Inferred" begin
     K = Wavenumber(k=50.0, θ=π/4)
     F = ComplexF64(1.0 + im)
     C = Configuration(F, K, O)
     try
-      @inferred dielectric(numerical_rb, C)
+      @inferred conductivity(numerical_rb, C)
       @test true
     catch
-      @warn "dielectric not inferred for $(nameof(typeof(numerical_rb)))"
+      @warn "conductivity not inferred for $(nameof(typeof(numerical_rb)))"
       @test_broken false
     end
     try
-      @inferred dielectric(ringbeam_rb, C)
+      @inferred conductivity(ringbeam_rb, C)
       @test true
     catch
-      @warn "dielectric not inferred for $(nameof(typeof(ringbeam_rb)))"
+      @warn "conductivity not inferred for $(nameof(typeof(ringbeam_rb)))"
       @test_broken false
     end
   end