src/beams.f90: document read_beam{0,1} formats
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Michele Guerini Rocco
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117
src/beams.f90
117
src/beams.f90
@ -7,6 +7,24 @@ contains
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subroutine read_beam0(params, unit)
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! Reads the wave launcher parameters for the simple case
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! where w(z) and 1/R(z) are fixed.
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!
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! The file should be formatted as follows:
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!
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! 1 f
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! 2 x₀ y₀ z₀
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! 3 w₁ w₂ z₁ z₂ φ
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!
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! where:
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! - f is the frequency (GHz)
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! - x₀, y₀, z₀ are the launcher position (mm)
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! - w₁,w₂ are the beam waists in the two principal directions (mm)
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! - z₁,z₂ are the positions of the foci in the two principal
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! directions (mm)
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! - φ is the of the ellipse (deg)
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!
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! Note: this case implies simple astigmatism, i.e. the
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! amplitude and phase ellipses in the transverse plane
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! are aligned.
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use const_and_precisions, only : pi, vc=>ccgs_
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use gray_params, only : antenna_parameters
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@ -22,7 +40,7 @@ contains
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! local variables
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integer :: u
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integer :: err
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real(wp_) :: ak0,zrcsi,zreta
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real(wp_) :: k0, w0(2), z0(2), z_R(2), phi
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u = get_free_unit(unit)
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@ -33,26 +51,50 @@ contains
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call exit(1)
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end if
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read(u, *) params%fghz
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read(u, *) params%pos
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read(u, *) params%w, params%ri, params%phi(1)
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read(u, *) params%fghz ! Wave frequency (GHz)
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read(u, *) params%pos ! Launcher position (Cartesian coordinates)
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read(u, *) w0, & ! Beam waists (in the ξ,η axes)
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z0, & ! Foci positions (in the ξ,η axes)
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phi ! Ellipse axes angle
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close(u)
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ak0 = 2.0e9_wp_* pi * params%fghz / vc
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zrcsi = 0.5_wp_ * ak0 * params%w(1)**2
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zreta = 0.5_wp_ * ak0 * params%w(2)**2
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! Wavevector k₀
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k0 = 2.0e9_wp_* pi * params%fghz / vc
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params%w(1) = params%w(1) * sqrt(1.0_wp_ + (params%ri(1)/zrcsi)**2)
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params%w(2) = params%w(2) * sqrt(1.0_wp_ + (params%ri(2)/zreta)**2)
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params%ri(1) = -params%ri(1) / (params%ri(1)**2 + zrcsi**2)
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params%ri(2) = -params%ri(2) / (params%ri(2)**2 + zreta**2)
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params%phi(2) = params%phi(1)
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! Rayleigh ranges in the ξ, η directions:
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! z_R = ½k₀w₀²
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z_R = k0/2 * w0**2
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! Beam widths in the ξ, η directions at z=0:
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! w² = w₀² (1 + z₀²/z_R²)
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params%w = w0 * sqrt(1 + (z0/z_R)**2)
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! Curvature in the ξ, η directions at z=0:
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! K = 1/R = (z-z₀)/[(z-z₀)² + z_R²]
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params%ri = -z0 / (z0**2 + z_R**2)
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! Ellipse axes angle
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params%phi = phi
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end subroutine read_beam0
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subroutine read_beam1(params, unit)
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! Reads the wave launcher parameters for the case
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! where w(z, α) and 1/R(z, α) depend on the launcher angle α.
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!
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! Format notes:
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! 1. The first two lines contain the frequency in GHz
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! and the number of rows.
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! 2. The rest of file is a table with the following columns:
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! θ, α, β, x₀, y₀, z₀, w₁, w₂, k₁, k₂, φ_w, φ_R
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! 3 The meaning of the columns is
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! - θ is the mechanical steering angle (useless)
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! - α, β are the poloidal and toroidal launch angles (deg)
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! - x₀, y₀, z₀ are the launcher position (mm)
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! - w₁,w₂ are the beam waists in the two principal directions (mm)
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! - k₁,k₂ are the wavefront curvatures in the two principal
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! directions (mm⁻¹)
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! - φ_w, φ_R are the angles of the amplitude and phase ellipses (deg)
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use gray_params, only : antenna_parameters
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use simplespline, only : spli, difcs
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@ -742,9 +784,13 @@ contains
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end subroutine read_beam2
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subroutine launchangles2n(params, anv)
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subroutine launchangles2n(params, N)
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! Given the wave launcher `params` computes the initial
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! wavevector `anv`, defined by n̅ = ck̅/ω, in cartesian coordinates.
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! wavevector N̅ = ck̅/ω.
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!
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! Notes:
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! 1. the result is in Cartesian coordinates;
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! 2. the beam is assumed to start in a vacuum, so N = 1.
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use const_and_precisions, only : degree
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use gray_params, only : antenna_parameters
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@ -753,31 +799,38 @@ contains
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! subroutine arguments
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type(antenna_parameters), intent(in) :: params
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real(wp_), intent(out) :: anv(3)
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real(wp_), intent(out) :: N(3)
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! local variables
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real(wp_) :: r, anr, anphi, a, b
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real(wp_) :: r, Nr, Nphi, a, b
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r = sqrt(params%pos(1)**2 + params%pos(2)**2)
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a = degree*params%alpha
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b = degree*params%beta
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R = hypot(params%pos(1), params%pos(2))
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a = params%alpha * degree
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b = params%beta * degree
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! Angles α, β in a local reference system
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! as proposed by Gribov et al.
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anr = -cos(b)*cos(a)
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anphi = sin(b)
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! N̅ in cylindrical coordinates using the poloidal
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! and toroidal launch angles.
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Nr = -cos(a)*cos(b)
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Nphi = sin(b)
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anv(1) = (anr*params%pos(1) - anphi*params%pos(2))/r ! = anx
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anv(2) = (anr*params%pos(2) + anphi*params%pos(1))/r ! = any
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anv(3) = -cos(b)*sin(a) ! = anz
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! Convert to Cartesian coordinates
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! Notes:
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! 1. The unit vectors in Cartesian coordinates are:
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! R^ = x^ cosφ + y^ sinφ
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! φ^ = x^ sinφ - y^ sinφ
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! 2. tanφ = y/x ⇒ { cosφ = x/√(x²+y²) = x/R
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! { sinφ = y/√(x²+y²) = x/R
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N(1) = (Nr*params%pos(1) - Nphi*params%pos(2)) / R
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N(2) = (Nr*params%pos(2) + Nphi*params%pos(1)) / R
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N(3) = -cos(b)*sin(a)
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end subroutine launchangles2n
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subroutine xgygcoeff(fghz, ak0, bres, xgcn)
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subroutine xgygcoeff(fghz, k0, Bres, xgcn)
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! Given the EC wave frequency computes:
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!
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! 1. vacuum wavevector `k0` (k₀ = ω/c),
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! 2. resonant magnetic field `bres` (qB/m = ω),
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! 2. resonant magnetic field `Bres` (qB/m = ω),
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! 3. adimensional `xgcn` parameter (X = ω_p²/ω² = nq²/ε₀mω²).
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use const_and_precisions, only : qe=>ecgs_, me=>mecgs_, &
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vc=>ccgs_, pi, wce1_
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@ -785,16 +838,16 @@ contains
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! subroutine arguments
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real(wp_), intent(in) :: fghz
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real(wp_), intent(out) :: ak0, bres, xgcn
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real(wp_), intent(out) :: k0, Bres, xgcn
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! local variables
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real(wp_) :: omega
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omega = 2.0e9_wp_*pi*fghz ! [rad/s]
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ak0 = omega/vc ! [rad/cm]
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k0 = omega/vc ! [rad/cm]
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! yg = btot/bres
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bres = omega/wce1_ ! [T]
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! yg = Btot/Bres
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Bres = omega/wce1_ ! [T]
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! xg = xgcn*dens19
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xgcn = 4.0e13_wp_ * pi * qe**2/(me * omega**2) ! [10^-19 m^3]
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@ -92,10 +92,7 @@ contains
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call xgygcoeff(params%antenna%fghz, ak0, bres, xgcn)
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! Compute the initial cartesian wavevector (anv0)
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! from launch angles α,β and the position x₀:
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! NR(α, β, x₀)
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! Nφ(α, β, x₀)
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! Nz(α, β, x₀)
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! from launch angles α,β and the position
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call launchangles2n(params%antenna, anv0)
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! Initialise the ray variables (beamtracing)
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