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07.10.2009 IPP - Garching Reflectometry Diagnostics and Rational Surface Localization with Fast Swept Systems José Vicente [email protected]
07.10.2009 IPP - Garching
Reflectometry Diagnosticsand Rational Surface Localization with
Fast Swept Systems
José Vicente
Motivation
Perform physics studies with help from reflectometry systems, namely the density profile systems, from AUG and JET.
Outline
Waves in plasmas Reflectometry: principles of operation
Density profile systems
AUG and JET systems Rational Surface Localization
Other applications/systems
Remember waves in plasmas...
Consider high-frequency electron oscillations (ions remain at rest)!
The plasma neutrality is broken and an electric field arises pushing electrons back to equilibrium while leading to a density perturbation…
Ee
E
x
electron displacement
electric field
force
Momentum eq.
Poisson eq.
Fluid continuity eq. xe
xee
vx
nnt
ne
Ex
vt
mEe
,
0
,
Remember waves in plasmas...
0
2
e
epe m
en
00
2
2
2
nm
enn
t e
e
Taking the time derivative yields the linear wave equation:
Cold Plasma!
Simple temporal oscillation with angular frequency:
Remember waves in plasmas...
t
E
cJB
t
BE
B
E
20
0
1
0.
/.
The well known solutions in vacuum, far from the source, are the plane waves, for E and B:
).cos(),( 0 wtrkEtrE ).(
0wtrkieEE
Remember waves in plasmas...The formal study of an uniform magnetized plasma finds that a solution to the Maxwell equations in the form of a e-plane wave is only possible if the wave vector and the frequency satisfy a dispersion relationship, which in the cold plasma approximation (all electrons have the same speed) is given by:
... where it is used the vectorial refractive index,
N = k c/
with N2 = N2 + N2
0
0
0
32
||
12
2
||212||
NNN
Ni
NNiN
Det
2
2
3
22
2
2
22
2
1
1
1
pe
ge
pege
ge
pe
ωω
ω
wikipedia !
2 electromagnetic modes for electron waves, and kB0 , but other modes are possible for instance for electrostatic conditions and/or ion species…
The solution gives two characteristic modes of propagation, the ordinary and extraordinary modes with different dispersion relations.
And we get that N2 = 0 condition (phase velocity becomes infinity) is satisfied for some cutoffs – the wave is reflected!
Remember waves in plasmas...
2
122 4
2
1pccR
2
122 4
2
1pccL
Reflectometry
103104105106107108109101010111012
10-2
102
100
10-310-410-510-610-710-810-9
10-10
101
103104105106107
f[Hz]
[m]
E[eV]
ion cyclotron emission
reflectometry electron cyclotron emission
coherent thomson scatteringinterferometry/polarimetry synchrotron radiation
visible light spectroscopy/ incoherent thomson scatteringvuv spectroscopy/xuv spectroscopy
soft x-ray spectroscopy/ neutral particle analysis
magnetics
fusion product diagnosticshard x-ray spectroscopy
atomic beam diagnostics
Microwave
Diagnostics
Reflectometry
ee
e
epe n
e
fm
m
en
2
20
0
2 )2(
Probing frequency
Take for instance the O-mode…
Cutoff density
(Cutoff density)
Reflectometry
Phase
Time of flight
)(),(2)( 0
)(
0
wdxxwNc
ww
wx
x
c
After propagation into the plasma and back, the reflected wave presents a phase shift.
This phase shift gives in fact an equivalent time delay, or group delay:
df
df
2
1)(
So, we “throw” waves at the plasma, wait for their reflection and measure:
Density ProfilesBoth phase measurement and time-of-flight measurement techniques may be applied to plasma profiles.
For O-mode operation, in which the cutoff frequency is solely a function of electron density, the group delay data (in the case of time-of-flight techniques) or a derivative of the phase delay data (in the case of phase measurement techniques) may be Abel-inverted to reconstruct the electron density profile of the target plasma.
The most common approach is a phase measurement technique called swept frequency modulation (FM) reflectometry, while two different time-of-flight techniques have been applied to this problem: amplitude modulation (AM) reflectometry and ultrashort pulse reflectometry (USPR).
from Textor-94
Density Profiles - FM
Main components
• Microwave Source (Sweep frequency)
• Transmission Line + Front-ends
• Detection System (e.g. Quadrature- phase scheme below)
Density Profiles - FM
Heterodyne detection allows the basic measurement to be of the fringe frequency resulting from the beating between the reference and plasma signals! This (with a sliding FFT e.g.) gives the group delay needed for profile reconstruction. 1
)( )(2
1
dt
dfff
df
dbf
Density Profiles - FM
From the group delay measurements inside the range of interest (frequency range) the cutoff layer positions are determined by an Abel inversion
cf
c
cc dfff
fc
fr0
22
1)()(
)(rnn ee
Probing frequency
Density Profile
Density Profiles – JET and AUG
Both systems measure up to ~ 12x1019m-3
JETBands Freq.Range LFS LFS HFS
K 16-25 - O OKa 25-36 - O OQ 33-50 X X/O OV 50-75 X/O X/O OW 75-110 X/O O -D 110-150 X - -
AUGReflectometry Access
•Just commissioned, profile reconstruction algorithms still being optimized.
•10 μs sweep time
•Edge to magnetic axis and beyond
•~ 15 years old (Q band detectors damaged, HFS mixer lost sensit/!)
•20 μs sweep time
Density Profiles - AUG
Plasma current
NBI and ICRH power
Core and edge line integrated density
Plasma stored energy
D-alpha
Density Profiles - AUG
Different diagnostics, Shifted profiles!
Density Profiles - AUG
Poor S/N in Q-band
Density Profiles - AUG
Density Profiles - AUG
Whole pedestal is probed!
Density Profiles - AUG
• ELM resolved profiles• Pedestal studies• Transport…
Density Profiles - JETW-band
- back wall, resonances and not pure X-mode are issues...
- shift in profiles compared with HRTS also present…
- equilibrium reconstruction?
Rational surface localization
L. Vermare, et al PPCF 2005
When MHD modes develop in the vicinity of rational surface, they can be used to give one or two points of the current profile.
Magnetic islands modify density profiles by involving a local flatness due to the reconnection of flux surfaces.
But an analysis based on jumps on the time of flight during fast sweeps is possible and more straightforward then through the “flatness” of the profiles!
Rational surface localization
F. Clairet, et al 2005
In addition to the jumps associated with magnetic islands, incoherent turbulence may produce random jumps, detected at random radial positions.
Radial positions retrieved by profile reconstruction.
Magnetic islands dynamics also possible to be studied (crossing of X and O points)
Rational surfaces calculated by equilibrium code.
Magnetic islands have to be present! (t=9, t=11)
Summary
Reviewed waves in plasmas (O-mode, X-mode) Reflectometry principles and measurements (phase or time of
flight) Density profile systems (FM-CW at AUG and JET) A different application – Localization of rational surfaces
Some characteristics: + local measurement, + high time resolution, - cannot look over local maxima, +- sensitivity to turbulence
