integrator - Instituto de Plasmas e Fusão Nuclear

Magnetics Diagnostics 

2 nd Advanced Course on Diagnostics and Data Acquisition 

Bernardo Brotas Carvalho 

bernardo@ipfn.ist.utl.pt 

http://ipfn.ist.utl.pt/EU-PhD/ 

Instituto de Plasmas e Fusão Nuclear 

Instituto Superior Técnico 

Lisbon, Portugal 

http://www.ipfn.ist.utl.pt 

B. Carvalho| Lisbon, February 2, 2010 | Diagnostics & Data Acquisition

General Principles 

• Magnetic measurements provide some of the 

most fundamental and essential information 

about a fusion plasma: 

– Iplasma, internal inductance, position and speed of 

current centroid, shape of boundary, thermal energy, 

currents in the magnet coils, and the strength of the 

magnetic fields confining the plasma 

– information about the internal characteristics of the 

plasma and about asymmetries caused by large-scale 

MHD instabilities 

– Halo Currents 

Author’s name | Place, Month xx, 2007 | Event 

2 B. Carvalho| Lisbon, February 2, 2010 | Diagnostics & Data Acquisition

General Principles 

• Essential for equilibrium reconstructions 

– Post-discharge full equilibrium codes 

– Real-time Plasma Shape and position control 

• Magnetic diagnostics are external, passive 

and ROBUST 

– The measurements remain valid and useful 

over the full range of plasma density and 

temperature as well as during large transient 

events (disruptions) 



Measurement of Magnetic Fields 

in Axisymmetric Configurations 

• The axisymmetric magnetic field in a 

cylindrical coordinate system (R, Z ,ϕ) can 

be expressed in terms of two scalar 

functions F and ψ: 

• This field can be separated in 

• Toroidal Field 

• Poloidal Field 



Magnetic and Current 

Poloidal Fluxes 

• The function ψ , “poloidal 

flux” (PF) is related to the 

magnetic field flux over 

one major circle at (R,Z) 

ψ R,Z = Ψ R,Z 

B 

Ψ R,Z = 

2π = R A φ (R, Z) 

B ∙ dS 

Z 

Flux per radian, 

also related to the 

toroidal component 

of the magnetic 

vector potential 

J pol 

• The function F, “poloidal 

current function” is related 

to the total current crossing 

a major circle at (R,Z) 

F R,Z = μ I pol R,Z 

I pol (R,Z)= 

Z 

2π = R B φ (R, Z) 

J pol 

∙ dS 

R 

R 



Toroidal Magnetic Field 

• Ampere’s Law 

• Poloidal component: 

• In vaccum =0 so Bϕ 

varies only with 1/R 

(no information from the 

plasma with external 

measurements) 

• Within plasma, Bϕ depends 

on poloidal currents internal 

to the plasma 

– A “diamagnetic loop” can 

measure changes in the total 

toroidal field 

Bϕ = F/R 

Diamagnetic 

Plasma 

Paramagnetic 

Plasma 



Poloidal Magnetic Field 

• Toroidal Component 

• Using Green’s Theorem 

∂Ω 

Z 

x’ 

r 

Plasma 

Ω 

External 

Coils 



Basic restrictions of the magnetic 

diagnostics for equilibrium reconstruction 

• Green’s Theorem with Ω 

bounded by the plasma and 

r→∞ 

1) Currents external to the 

plasma in coils or other 

conductors. 

2) Poloidal flux at the plasma 

boundary (constant) 

Z 

x’ 

Ω 

∂Ω 

r 

Plasma 

r→∞ 

K φ 

⨂ 

B t 

External 

Coils 

3) Normal derivative of Poloidal 

flux at the plasma boundary (B t ) 

ψ = Cnst 

External magnetic 

Term “3” is equivalent The surface current K φ measurements can determine 

to a given surface 

is itself equivalent to 

the poloidal flux anywhere in Ω 

current distribution K φ 

many internal current 

and on the equivalent surface 

at the plasma 

distribution inside the 

current K. BUT can NEVER 

boundary: μ 0 K φ = B t Plasma J φ (r) 

distinguish different internal 

current distributions 

8 B. Carvalho| Lisbon, February 2, 2010 | Author’s Diagnostics name | Place, & Data Month Acquisition xx, 2007 | Event

Electrostatics Case 

The Electric Field outside the Sphere is the same for a given surface charge density 

or other infinite volume charge distributions 

Plasma 

ω 

K(ω) 



Grad-Shafranov Equilibrium Equation 

• Combining equation for PF with magnetic 

force balance gives G-S equation 

inside the plasma: 

• GS gives additional constraint on the 

magnetic field within the plasma but also 

introduces another unknown scalar function: 

the pressure 

• We need to make some assumptions 

p(ψ) and F(ψ) to obtain full plasma 

equilibrium solution 


Determination of Plasma 

Shape and position 

• Taking measurements of the Poloidal Flux and poloidal 

Magnetic fields near the Wall, plus the currents in external 

Coil allows extrapolation of ψ(R,Z) until the plasma 

boundary 

• Plot the contours of ψ(R,Z)=Cte and then find the Last 

Closed Flux Surface (LCFS), or the the separatrix in divertor 

tokamaks 

Flux Loops 

LCFS 

Magnetic Probes 

Divertor Tokamak 



Other Integral quantities given 

from Magnetics measurements 

• Total plasma current I p 

• Poloidal beta: 

– Proportional to the thermal energy of 

the plasma! 

• Plasma Normalized Internal 

inductance: 

– related to the first moment of the 

current density distribution 

• “Shafranov shift” 

-length of a poloidal 

contour at the plasma 

surface 

Plasma LCFS 

“Shafranov Shift” 



Inductive Sensors 

(Basic types) 

Mag. Flux on the Sensor Loop 

Signal on Sensor 

Signal from sensor must be integrated 



Axisymetric Poloidal Flux Loops 

Bp 

In Iron Core Tokamak 

with Ohmic Heating most 

of the poloidal flux is on 

the core itself 

To improve the sensivity one loop is 

chosen as reference and is subtracted 

from other loops: Φ net = 2π(ψ − ψ ref ) 

The unintegrated voltage 

signal from a flux loop 

is the local one-turn 

loop voltage, V loop , driving 

the plasma current 


Magnetic Field Probes 

• Probe measures components of the 

local magnetic field strength 

• Usually solenoidal, with dimensions 

small compared to the gradient scale 

length of the magnetic field 

Probes should be located on the plasmafacing 

side of the vacuum vessel wall. 

Must be oriented to measure the field 

tangential to the wall; otherwise, eddy 

currents in the wall will attenuate the 

high-frequency part of the signal. 

Φ probe 

= N A B ∥ 

Shielding of the tangencial field 

by the conductive wall. 

is the characteristic time for the 

magnetic flux to diffuse through 

wall 


Saddle Loops 

Legs in toroidal 

direction 

Legs in poloidal 

direction 

• Can be viewed as a 

large-scale magnetic 

probe for the magnetic 

field normal to the 

surface: 

• Or as probes measuring 

flux difference: 

Often used for detecting nonaxisymmetric 

fields caused by nonrotating MHD 

instabilities. 

This measurement is most sensitive to 

instabilities with low frequencies since at 

high frequencies the normal component of 

the field is shielded by the wall 

• Also used for active 

control of MHD plasma 

modes (eg. RFX, 

Padova) 



Diamagnetic Loops 

At low beta the change in the total 

toroidal flux is small. 

• A diamagnetic loop measures the 

toroidal magnetic flux for the 

purpose of estimating the thermal 

energy of the plasma. 

• Normally located in a poloidal 

plane in order to minimize 

coupling to the poloidal field. 

A reference signal equal to the vacuum 

magnetic flux is usually subtracted, 

with 



Rogowski Coil 

Ip 

The Conducting path from one end of the 

coil returns along the axis to the other 

end 

• The Rogowski coil measures 

electric current flowing through 

the enclosed surface 

(e.g. plasma, plasma + vessel, 

external coils, passive 

conductors, Halo Currents, etc.) 

• The total flux linked by all turns is 

proportional to the contour 

integral: 

Φ Rog ~ B dl = μ 0 I 

• Signal is proportional to current 

time derivative 

V = −Nμ 0 n A dI 

dt 



Integration of signals from 

inductive sensors 

• To obtain the fluxes and magnetic field values 

from inductive sensors we must integrate the 

signal in time: 

V out = − 1 τ 

V in dt = − Φ τ 

• Typical loop flux values vary from few mV.s to 

few V.s (eg. Iron core), so integrator circuits are 

used with τ equal to 1 ms to 1 s 

Simple Passive Integrator 

The approximation fails for timescales 

comparable to or longer than τ 



Active Integration 

V offset 

But now a new pratical problem: 

“Integrator drift” 

Exemple: for RC = 10ms a 100 μV offset 

integrates to a 0.1 V after 10 s 

The gain is similar to the passive 

integrator but now the timescale is 

increased for ~RC to ~G* RC ( 1 to 10 s) 

Feedback 

Filter 

Basic compensation circuit 



Pick Up Coil 

Advanced Analog Integrators 

Automatic drift-compensation: Measurement 

of drift before integration, store and 

compensate offset during integration 

Drift can be reduced down to 

several 0.1mVs / 1000s 

Reset 

But worse values if signal 

is applied during drift 

compensation! 

Common mode rejection 

Asymmetric input! 

- 

+ 

S/H 

ADC 

Drift achieved in Tore Supra: 

< 135 μVs / 1000 s 

Auto Offset Correction 



Pick Up Coil 

Digital (chopper) integrator 

Clock 

ADC 

Digital Input 

Chopper 

Num. Rectifier 

+ Integration 

Amp 

ADC 

AC coupling allowed! 

• Dynamic range limited by input stage 

• Not affected by input stage semiconductors 

• No 1/f noise 

• Complex offset correction algorithms feasible 

• Very simple consumer electronics! 



Pick Up Coil 

W-7X prototype Integrator schematic 

Low pass 

(avoid resistors, 

huge thermovoltage) 

1 

2 

Clock 

Butterworth low pass, 

removes spikes by charge injection 

2 

1 

- 

+ 

+ 

1 

2 

+ 

- 

- 

Input Chopper 

Symmetric chopper stage based 

on CMOS switch MAX4644 

R on < 3Ω 

Instrumentation 

Amplifier 

Clock 

USB Power Supply 

Low charge injection 

Prototype (still in use) 


W-7X prototype Integrator drift 

• 100 s drift 

compensation 

• 1000 s run 

“Cold Integrator” 

• Drift: 

< 70 μVs / 1000 s 



Diagnostics with non-Integrated 

signal from Inductive probes 

• Vertical Speed of Plasma current centroid 

– Linear combinations of flux and field probes 

– Used as controllabe variables for active control 

• MHD Instabilities detection and control 

– “Mirnov coils”, poloidal or toroidal arrays of 

probes oriented to measure poloidal 

component, inside the vacuum vessel 

Differential connection of 

magnetic probes, for 

detection of nonrotating 

MHD modes or . 

Array of 12 Mirnov Coils in 

ISTTOK 



MHD Instabilities diagnostics 

• Analyses Techniques: 

– Spectrogram (Fourier analysis of sucessive 

short-time windows 

Spectrogram of magnetic probe signals in JET, showing the time 

evolution of the amplitudes and frequencies of several tearing 

modes. 


MHD Instabilities diagnostics: 

Other techniques 

• Wavelet analysis 

• Hilbert transform 

• Singular Value Decomposition (SVD) 

Experimental data from T-10 shot no. 

21576: 

(a) Hilbert spectrum; 

(b) Spectrogram 

(c) wavelet scalogram. 

a) 

c) 

b) 



MHD mode detection 

• Mode number are determined by the 

phase shift, (by Fourier Analysis) between 

equally or varied separated Mirnov coils 

Identification of the mode number 

and polarization of a compressional 

Identification of poloidal mode 

Alfvén eigenmode in NSTX, 

number m=4 for a tearing 

showing phase shift and amplitude 

mode in TFTR, showing the 

versus toroidal angle. 

phase shift of Mirnov loop 

The phase shift between toroidally 

separated coils gives a toroidal 

signals versus poloidal angle. 

mode number n = 7 


Nonrotating Modes 

• Nonrotating modes are most 

commonly detected with toroidal 

arrays of saddle coils (loops 

oriented to measure the radial 

field) 

– Low frequencies involved and the 

field perturbation of the mode 

penetrates the vacuum vessel 

Time evolution of an RWM in 

JT-60U, showing contours of 

the time derivative of the 

radial field perturbation 

measured with a uniformly 

spaced toroidal array of eight 

saddle coils 



Non Inductive Sensors 

• Hall Probes 

– relatively simple and inexpensive 

• Resistive Shunts 

– measuring “halo” currents flowing between the plasma and 

plasma-facing components 

• Faraday rotation current measurements 

Example of Hall 

Probe for ITER 

V H = 1 I B 

qn a 

Schematic overview of a fiber-optic 

Schematic figure of a Hall probe in a Hall coefficient, is a Faraday rotation measurement 

magnetic field B, 

property of the device, to be used for the 

with I the injected current and V H the material 

measurement of the plasma current 

resulting Hall 

in ITER 

30 voltage. 

B. Carvalho| Lisbon, February 2, 2010 | Author’s Diagnostics name | Place, & Data Month Acquisition xx, 2007 | Event

Burning plasma experiments/ITER 

ITER will be the burning plasma experiment where 

all the knowledge on burning plasma diagnostics 

will converge 

Relative to existing machines, on ITER diagnostic 

components will be subjected to (relative to JET) 

• High neutron and gamma fluxes (up to x10) 

•Neutron heating (essentially zero) 

•High fluxes of energetic neutral particles 

from charge-exchange processes (up to x5) 

•Long pulse lengths (up to x100) 

•High neutron fluence (>10 6 !) 



ITER diagnostics 

Functional requirements 

“to provide accurate measurements of plasma behaviour and 

performance.” 

3 categories of measurement parameters 

• Group 1 Machine protection and Basic machine control 

(machine operation unable without this group) 

• Group 1b advanced plasma control 

(machine advanced operation unable without this group) 

• Group 2 evaluation and physics studies 

(machine operation able without this group) 



Magnetic Diagnostic Set for ITER 

Total : 

Location n g Type Number 

In-vessel sensors: 

Behind blanket 

modules, fixed on 

VV inner skin 

Divertor 

Ex-vessel sensors 

Fixed on VV outer 

skin 

Inside TFC case 

(T=4K) 

Radiation/Dose 

(cm -2 s -1 ) / MGy 

3. 10 12 

Pick-up coils 186 

Rogowski 

(halo current) 

360 

Flux loops 220 

High freq 

coils 

>300 


Rogowski 

(halo current) 

48 


Steady state 

sensors 

120 

Flux loops 5 


33 B. Carvalho| Lisbon, February 2, 2010 | Diagnostics & Data Acquisition 

500 

1. 10 13 

1700 

1. 10 13 

1700 

1.5 10 10 

2.5 

1. 10 10 

1.7 

1. 10 12 

340 

3. 10 12 

1000 

3. 10 12 

1000 

1. 10 10 

3.4 

2. 10 9 

0.7 

Optic fibre 12 

Rogowski 

(I plasma) 

3 

~ 1700 sensors, 19 types, >300km of cable

ITER Magnetic Poloidal Set 



MHD saddle loops mounted on 

all 9 machine sectors, made from 

mineral insulated (MI) cable 



Main Technogical Chalenges 

• Long plasma pulse length (400s – 3000s): 

• Integrator Drift and induced EMF Issues 

• Radiation Effects- Prompt: 

• RIC - Radiation Induced Conductivity 

• Loads the signal during the pulse. Can be mitigated by choice of 

material 

• RIEMF - Radiation induced electromotive force 

• Both neutrons and gammas, induces currents between the sensor wire 

and its surroundings. The typical magnitude is in the range 0.1-10 V 

• RIED- Radiation induced electrical degradation 

• The insulator material, including impurity content, is important and even 

different samples of the same material can behave differently 

• TIEMF - Thermally induced electromotive force 

• Produces a non-zero thermo-electric EMF due to manufacturing 

imperfections 



Main Technological Chalenges 

• Radiation Effects- Long Term: 

• RIED- Radiation Induced electrical degradation 

• The insulator material, including impurity content, is 

important and even different samples of the same 

material can behave differently 

• RITES - Radiation Induced ThermoElectric Sensivity 

• Nuclear heating supplies the temperature differences 

• Variety of effects can supply the material propety 

changes that generate themocouples 

• Installation and Integration problems 

• Design qualified for the machine lifetime > 20 years

integrator - Instituto de Plasmas e Fusão Nuclear

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