From 130db108c041e8bd049e9a2a6eeb0bc371f1acc0 Mon Sep 17 00:00:00 2001
From: James Cook <cookjws@gmail.com>
Date: Sun, 5 Nov 2023 14:50:40 +0000
Subject: [PATCH] put back curlcurl but with minus sign in both places

---
 src/Tensors.jl      |  3 ++-
 src/Wavenumbers.jl  |  4 ++--
 test/Wavenumbers.jl | 12 +++++++-----
 3 files changed, 11 insertions(+), 8 deletions(-)

diff --git a/src/Tensors.jl b/src/Tensors.jl
index 483c9e6..fb25188 100644
--- a/src/Tensors.jl
+++ b/src/Tensors.jl
@@ -189,11 +189,12 @@ end
 Calculate the tensor representing the linear Maxwell-Vlasov set of equations.
 The determinant is zero when the wavenumber and frequency represent a solution
 to the linear Maxwell-Vlasov system of equations for these species.
+Note that the curlcurl operator keeps track of the factor of -1 from im^2.
 """
 function tensor(plasma::AbstractPlasma, config::Configuration,
     cache::Cache=Cache())
   ϵᵢⱼ = dielectric(plasma, config, cache)
-  return ϵᵢⱼ + kkT_Ik²(config.wavenumber) * (c₀ / config.frequency)^2
+  return ϵᵢⱼ - curlcurl(config.wavenumber) * (c₀ / config.frequency)^2
 end
 
 """
diff --git a/src/Wavenumbers.jl b/src/Wavenumbers.jl
index 614341b..eaf5c1d 100644
--- a/src/Wavenumbers.jl
+++ b/src/Wavenumbers.jl
@@ -47,9 +47,9 @@ Base.angle(K::Wavenumber) = propagationangle(K)
 
 @inline cartesian_vector(K::Wavenumber) = @SArray [perp(K), 0.0, para(K)]
 
-@inline function kkT_Ik²(K::Wavenumber)
+@inline function curlcurl(K::Wavenumber)
   k = cartesian_vector(K)
-  return k*k' - dot(k, k) * I
+  return sum(x->x^2, k) * I - k*transpose(k) # defend against complex k
 end
 
 Base.abs(K::Wavenumber) = sqrt(abs2(K))
diff --git a/test/Wavenumbers.jl b/test/Wavenumbers.jl
index c37029f..63f5747 100644
--- a/test/Wavenumbers.jl
+++ b/test/Wavenumbers.jl
@@ -48,12 +48,14 @@ const k0 = -1.234
   end
 
   @testset "curl curl operator" begin
-    K = Wavenumber(wavenumber=k0, propagationangle=π/4)
-    k_x_k = LMV.kkT_Ik²(K)
-    c = LMV.cartesian_vector(K)
+    for k1 in (k0, k0 + im)
+      K = Wavenumber(wavenumber=k0, propagationangle=π/4)
+      ∇x∇x = LMV.curlcurl(K)
+      c = LMV.cartesian_vector(K)
 
-    x = [0.0 -c[3] c[2]; c[3] 0.0 -c[1]; [-c[2] c[1] 0.0]]
-    @test all(x*x .== k_x_k)
+      curl = im * [0.0 -c[3] c[2]; c[3] 0.0 -c[1]; [-c[2] c[1] 0.0]]
+      @test all(curl * curl .== ∇x∇x)
+    end
   end
 
   @testset "Costructor wavenumber propagationangle" begin