A synthetic synchrotron diagnostic for runaways in tokamaks Mathias - - PowerPoint PPT Presentation
A synthetic synchrotron diagnostic for runaways in tokamaks Mathias Hoppe 1 Ola Embrus 1 , Alex Tinguely 2 , Robert Granetz 2 , Adam Stahl 1 , Tnde Flp 1 1 Chalmers University of Technology, Gothenburg, Sweden 2 PSFC, Massachusetts
Mathias Hoppe1
Ola Embréus1, Alex Tinguely2, Robert Granetz2, Adam Stahl1, Tünde Fülöp1
1 Chalmers University of Technology, Gothenburg, Sweden 2 PSFC, Massachusetts Institute of Technology, Cambridge, Massachusetts
diagnostic
parameters
Total power per pixel, per frequency interval dω: dIij dω (x0, ω) =
dA
dn ×
× ˆ
n · n r 2 f(x, p)δ
r
r − n
d2P(x, p, x0, ω)
dωdΩ Detector parameters A = Detector surface, n = Line-of-sight
ˆ
n = Viewing direction x0 = Detector position d2P/dωdΩ = Angular and spectral distribution of synchrotron radiation, f(x, p) = Distribution of runaways, Particle parameters r = |x − x0| = Distance between camera and particle.
Larmor radius ≪ B/|∇B| x X
Three transformations
dxdp ≈ dXdpdp⊥dζ
φ R z
Three transformations
dxdp ≈ dXdpdp⊥dζ
dX = R dRdzdφ
ρ φ τ
Three transformations
dxdp ≈ dXdpdp⊥dζ
dX = R dRdzdφ
(R, z) → (ρ, τ),
◮ ρ: Major radius of particle in the midplane, at beginning of orbit ◮ τ: Orbit time (a poloidal parameter)
Distribution function independent of:
Guiding-center distribution specified along the line τ = φ = 0 (outer midplane). dIij dω =
dA
dn
× ˆ
n · n r 2 fgc(ρ, p, p⊥)δ
r
r − n d2P(ρ, p, p⊥, x0, ω) dωdΩ
Angular and spectral distribution of synchrotron radiation: d2P dωdΩ = 3e2β2γ6ωB 32π3ǫ0c
ω ωc 2 1 − β cos ψ β cos ψ 2 × ×
2/3(ξ) + (β/2) cos ψ sin2 ψ
1 − β cos ψ K 2
1/3(ξ)
synchrotron images and spectra
synchrotron images and spectra
equations of motion using RKF45 in numeric magnetic geometry
synchrotron images and spectra
equations of motion using RKF45 in numeric magnetic geometry
runaway distribution function
synchrotron images and spectra
equations of motion using RKF45 in numeric magnetic geometry
runaway distribution function
with sufficient resolution
show significant difference in spectrum.
specified explicitly in
HF-side.
[1] A. Stahl, et. al. PoP 20, 093302 (2013).
Magnetic geometry: Alcator C-Mod, 3-8 T
range
below midplane Varied parameters:
Other parameters: Beam radius 16 cm Pitch angle 0.15 rad Spectral range 500-1000 nm Magnetic field 3-8 T Camera elevation −21 cm
E = 10 MeV E = 25 MeV E = 40 MeV E = 55 MeV
0% 20% 40% 60% 80% 100%
Other parameters: Beam radius 16 cm Energy 30 MeV Spectral range 500-1000 nm Magnetic field 3-8 T Camera elevation −21 cm
θp = 0.02 rad θp = 0.10 rad θp = 0.18 rad θp = 0.26 rad
0% 20% 40% 60% 80% 100%
Small pitch angle = small GC cone
= ⇒ small chance of reaching
detector
θp = 0.02 rad
Large pitch angle = large GC cone
= ⇒ greater chance of reaching
detector
θp = 0.18 rad
Other parameters: Beam radius 16 cm Energy 30 MeV Pitch angle 0.15 rad Spectral range 500-1000 nm Magnetic field 3-8 T Camera elevation −21 cm NOTE: Magnetic axis at R = 68 cm. Particles at R 72 cm are invisible in this configuration.
72 cm 74 cm 76 cm 78 cm 80 cm 82 cm 84 cm
[2] M. Landreman, et. al. CPC 185, 847 (2014). [3] A. Stahl, et. al. NF 56, 112009 (2016).
(Distribution function)
(Emitted radiation)
axisymmetric magnetic configurations
axisymmetric magnetic configurations
⇒ crucial to be clear about
how the runaway distribution is specified.
axisymmetric magnetic configurations
⇒ crucial to be clear about
how the runaway distribution is specified.
synchrotron radiation.
axisymmetric magnetic configurations
⇒ crucial to be clear about
how the runaway distribution is specified.
synchrotron radiation.
distribution from image.
Other parameters: Beam radius 16 cm Energy 30 MeV Pitch angle 0.15 rad Spectral range 500-1000 nm Magnetic field 3-8 T
z = −21 cm z = −14 cm z = −7 cm z = 0 cm
0% 20% 40% 60% 80% 100%