euratom tore supra g. bosia “matching iter-like structures” cadarache, 2-22 - 2005 matching...

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G. Bosia “Matching ITER-like structures” Cadarache, 2-22 - 2005

Matching ITER-like structures

G. Bosia

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Introduction From a power transfer point of view, an IC array can be described as a multi-primary transformer, inductively coupled between themselves and to two secondaries, ( plasma and vessel), also mutually coupled, one of which (the plasma) has variable electrical parameters.

Mp

Rp

Xp Mv

Rv

Xv

The two secondary currents can be “reflected “ in the primaries and the result is a N x N matrix problem of the type :

where ZL is the so called “plasma impedance matrix”, with elements describing array, plasma and vessel electrical parameters, and including all couplings and asymmetries .

Z L I V

The problem of matching the power sources ( Vk = R0 Ik) leads to an eigenvalue problem of the type

where R0 is a diagonal matrix.

Z L R 0 I 0

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Control of currents flow in a generic IC array

This represent the fact that the total RF power within in the vessel must go somewhere, and if it is not dissipated in the plasma or in the vessel it comes back to the sources and, depending of the vectorial relations between sources, may choose one or more of them as a load.

The conditions for the solution of the problem are easy to compute for a 2x2 matrix, somewhat difficult already for a 4x4 matrix, overhelming for a 24x24 element matrix describing the ITER array

.

The equation represents an over-constrained system with no general solution, unless:

1) the impedance elements of the primaries are suitably modified by combinations of auxiliary reactances (matching elements).

2) inequalities between the real parts of diagonal and not diagonal terms of the resulting matrix are fulfilled.

Z L R 0 I 0

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Control of currents flow in a generic arrayThe fast wave physics is related to magnetic coupling, i.e. to the pattern of the array currents. Wave damping in the bulk plasma is related to k// and k symmetric spectra

and a asymmetric k// spectrum is required CD.

Single strap

V = (Ls+ Lf) I

I V

In an array where the elements are individually powered, the strap current can be controlled

The plasma edge response is related to the array current pattern (sheaths) and not so much to the global voltage pattern. RF voltage is however locally important, since the electric field should not exceed the local “ vacuum” dielectric strength and excessive particles acceleration and at the limit voltage breakdowns

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ICH untuned poloidal array elements

An untuned array is proposed also for ITER

V = (Ls+ Lf/3+ Lf/2) I

V = (Ls+ Lf/2+ Lf/2) I

V

In most of the present IC systems, two- strap untuned poloidal array are used to reduce the on-plasma voltage

Oddly enough, in these systems, the pattern of the currents coupled to the plasma is not controlled.

In an untuned poloidal array, an even power division is possible only if both a array and load are symmetric and this on a very limited frequency band.

Therefore the radiation spectrum is load and frequency dependent, and it is likely to be affected by local dielectric properties of the “vacuum” at the first wall

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ICH tuned poloidal array elements

V

V = (Ls+ Lf) I

A good level of control of the poloidal currents is possible in tuned poloidal arrays such as the Resonant Double Loop (RDL)

Here the control of the reactive part of the current is possible by making use of the tuning capacitors.

In the ITER-like (ILS) structure, currents are

controlled to be complex conjugate, to

optimize load resilience

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Matching and array currents control

• A primary requirement in IC operation is to match the array, for an efficient power transfer. This is done by adding “tuning” reactances in the primary circuits, in general variable to cope with frequency changes.

• In a relatively complex array such as the ITER array it is an advantage to minimise the number of tuning components.

• A R-L isolated load can be perfectly matched to a resistive impedance by using a series/parallel combination of two reactances and, in an array, two more are in principle needed to decouple two neighbour elements.

• The number of tuning elements can be reduced if some symmetry can be claimed in the impedance matrix. In most tokamak applications toroidal symmetry is assumed.

• A tight control of the currents in the array elements helps in preserving symmetry in the array and reducing the number of tuning elements

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Active array radiation spectrum control, by feedback

• Substantial reductions in the number of the tuning components, simplification in matching acquisition and upholding and (in IL structures) load resilience, can be obtained if the array current pattern is feedback controlled.

• This has the additional important advantage that the array radiation pattern is preserved against load changes.

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What plasma impedance matrix should we expect in ITER?

We have for the moment only partial answers :

• In vacuum

• On a “ dielectric” plasma . (R = 200 + 200 i)

To answer this question an accurate description of how the RF power is scattered back from the plasma to the array is needed

this is affected :

•by the dielectric properties of the scrape off plasma

•by the antenna geometry

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2X2 array impedance matrix in vacuum

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2X2 array impedance matrix with dielectric plasma

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(As)symmetries of Z matrix induced by the target medium : summary

(As)symmetries of Z matrix induced by the target medium : summary

•Antenna = 22 array, 4 identical poloidal straps.•All symmetries verified with ICANT.

10 independant elements / 16

6 independant elements / 16.



Magnetized plasma, tilted B0

Magnetized plasma,

toroidal B0

Anisotropic

Dielectric, tilted B0

Vacuum =dielectric with

toroidal B0


6 independant elements / 16.



Magnetized plasma, tilted B0

Magnetized plasma,

toroidal B0

Anisotropic

Dielectric, tilted B0

Vacuum =dielectric with

toroidal B0

11121314

12111413

13141112

14131211

ZZZZ

ZZZZ

ZZZZ

ZZZZ

11121314

12222313

13232212

14131211

ZZZZ

ZZZZ

ZZZZ

ZZZZ

11123141

12114131

13141112

14131211

ZZZZ

ZZZZ

ZZZZ

ZZZZ

11213141

12223231

13232221

14131211

ZZZZ

ZZZZ

ZZZZ

ZZZZ

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Reduction of apparent interstrap coupling• It can be shown that the effects of inter-strap coupling can be reduced by shielding the straps by

means of toroidal and poloidal septa. However the currents induced in the septa modify the radiation spectrum of the array with a tendency of reducing the apparent plasma coupling.

20 40 60 80 0.2

- 0.1

0

0.1

0.2

Frequency (MHz)

S12

/ S

1 (r

etra

cted

sep

tum

)

20 40 60 800.02

0.01

0

0.01

0.02

Frequency (MHz)

S

12 /

S11

(fu

ll s

eptu

m)

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ITER-like structure : Simple (ITER Reference Design) case

R1

X1

R2

X 2

R0 + i X0

I1

I2

Rs R0 i X1

R0 i X0

R0 i X0.

Rs R0 i X2

I1

I2

0

X1 Xs1 X0 XC1 X2 Xs2 X0 XC2

If, in addition, we impose X0 0

Rs R0 i Xs1 Xsm XC1

R0

R0

Rs2 R0 i Xs2 Xsm XC2

I1

I2

0

XCM1

2XC1 XC2

I1MV

Rs i Rs 2 R0 Rs XCM1

2XC1 XC2

XM 0 I2MV

Rs i Rs 2 R0 Rs

XM Rs 2 R0 Rs

IinV

R0XCM Xs XM

XCM Xs XM

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Resilience to load variations An “ideal” ITER-like structure is resilient to load variations if it is matched to an input resistance R 0 typically 5 times the load resistance R s

S max1

S max0

X M0R M

1.35 2.69 4.03 5.36 6.71

1.25

1.5

1.75

2

Load resistance (ohm)

Volta

ge s

tand

ing

rwav

e ra

tio

R0= 30

R0= 22

R0= 14

R0= 6

.

Z0 = R0+1i X0

XC1

XC2

Z1 = Rs1+1i Xs1

Z2 = Rs2+1i Xs2

It was suggested 1) that the load resilience would be impaired by the inductive coupling between straps.

1) A. Messsiaen, 15th Topical Conference on Power Application to Plasmas (2003)

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ITER-like structure : General case

R1

X1

R2

X 2

Rm1+i Xm1

Rm2+i Xm2

R 1 1i X 1

R m1 1i X m1

R m2 1i X m2

R 2 1i X 2

I 1

I 2

0

R0 + i X0

I1

I2

Rk Rsk R0

Xk Xsk X0 XCk

Rmk Rsm2 R0

Xmk Xsm1 X0

Order of magnitudes: (Rs, Xs Rsm, Xsm are the arithmetic average of Rsk, Xsk Rsmk, Xsmk and Rs, Xs Rsm,

Xsm the asymmetries.

R0~ 5 X0 ~ 0 Rs< 1 Xs ~ 20 Rsm< Rs<< R0 Xsm< Xs but not <<X0

Rsk< Rs<< R0 Xsk<< Xs Rsm< Rs<< R0 Xsm<< Xsmk

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ITER-like structure: General case (approximate)If Rs << R0 , Rsm << R0 , Xs << Xs , Xsm < Xs but not << X0

Rs R0 i X1

R0 i X0 Xsm

R0 i X0 Xsm

Rs2 R0 i X2

I1

I2

0

Rs1

2Rs1 Rs2 Rs

1

2Rs1 Rs2 X1 Xs1 X0 XC1

X2 Xs2 X0 XC2If, in addition, we impose Xsm X0 0

Rs R0 i Xs1 Xsm XC1

R0

R0

Rs2 R0 i Xs2 Xsm XC2

I1

I2

0

XCM Xs Xsm XM I1MV

R0 i Xsm

R0

Rs i Rs 2 R0 Rs

XCM Xs XMI2M

V

R0 i Xsm

R0

Rs i Rs 2 R0 Rs

XCM1

2XC1 XC2

IinV

R0 i XsmRs

1

2XC1 XC22

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Conclusions on matching a single ILS

The number of necessary tuning elements is however reduced to three or two if the ILS is symmetrically loaded and internal not-conductive coupling remain within specific limit.

1st message:

If you design your ILS with the two half sections heavily coupled, (more than -15dB) it will cost you one more tuner.

An ILS, however asymmetrically loaded and internally non conductively coupled, can always be perfectly matched in conditions of optimum load resilience, by using less than four tuning reactances (which is the minimum legal number for resonantly tuning two isolated straps).

2nd message (demonstrated in the appendix of the paper)

If you randomly design your ILS it will cost you two tuners per strap

3th message

If the ILS mismatch is small, and therefore line voltage and losses are small, re-tuning can be

performed at the generator end.

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Preserving load resilience by control of the ILS currentsThe admittances in the two half sections of an arbitrarily coupled and loaded ILS can be feedback controlled to be complex conjugate, independent of load asymmetry and coupling, by using the two tuning capacitors. The capacitors should be adjusted to:

where Rs, Xs, Rsm, Xsm XC, and Rs, Xs, Rsm, Xsm XCare arithmetic averages and asymmetries of the matrix elements isthe conjugate angle and R0 =1/ Y0 is the (real and mismatched ) input resistance .

In asymmetrically loaded/coupled circuits, a voltage unbalance is associated with the symmetry of the currents: This is however irrelevant to the heating process with the fast wave, and simply sets a power limit to the operation

XC Xs Xsm tan ( ) Rs Rsm

XC Xs Rs

tan ( )Rs Xsm Rsm Rs

Rs Xsm Rs Rsm

R0 cos ( ) Rs Rsm sin ( ) Xs XC Xsm

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Generic layout of a tuned ILS

Pretuner Trimmer Decoupler

Decoupler

Isolator RF source

Main Transmission

Line

Load end Source end

ILS

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Functions of the Pre-tuner

• The conjugate angle is load dependent and it increases with the load power factor. This conditions provides the optimum load resilience, independent of loading and coupling, and it corresponds to perfect match for an ideal ILs.

• The electrical behaviour of the circuit is uniquely determined, and the feedback controlled ILS behaves as a load dependent resistive impedance

Zin ~ R0(Rs, Xs, Rsm, Xsm XC,,Rs, Xs, Rsm, Xsm).

• The function of the Pre-tuner is to feedback control the input admittances to be complex conjugated, by using the tuning capacitors.

• The control loop conditions are :

Re(Yin1) - Re(Yin2) = 0 and Im Yin1)+ Im(Yin2) = 0

or equivalently

Re(I1/Iin)- Re(I2/Iin)=0 and Im(I1/Iin)+Im(I2/Iin)=0

• If the impedance matrix is reasonably diagonal and symmetric (as for example in the case of ITER (R0 = 4 kp ~ 0.01 and Xs ~ 20 the mismatch is low and in general compatible with the power source specifications

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Functions of the ILS Pretuner

• For higher coupling coefficients and asymmetries, the mismatch is eliminated by a two reactance trimmer

m

34 36 38 40 42

34

36

38

40

42

33.8 38.8 C1 (pF) 43.8

kp = 0.0443.8

C2

pF

38.8

33.8

m

34 36 38 40 42

34

36

38

40

42

kp = 0.0

(Arg(I1) - Arg(Iin) + (Arg(I2) - Arg(Iin) = 0

33.8 38.8 C1 (pF) 43.8

|I1|- |I2| = 0

(Arg(I1) - Arg(Iin) + (Arg(I2) - Arg(Iin) = 0

|I1|- |I2| = 043.8

C2

pF

38.8

33.8

• As the both module and phase of the currents are vectorially controlled, adjacent array elements can be phased in self decoupling “dipole” and “monopole” conditions. If this is done with adequate accuracy, the array “phase instability” is avoided.

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• This behaviour applies to all linear networks fed by multiple sources. It is not at all typical of ILS arrays, and it has been studied before for the JET A1 phased antennas within the program of ICH minority current dive.

1) G. Bosia, J.Jacquinot, “Phased Antennas Arrays for Fast Wave Power Generation” , Proc IAEA Technical Committee Meeting on Fast Wave Current Drive in Reactor Scale Tokamaks, pp 471- 495 Arles (1991)

Coupling effects on networks of Coupling effects on networks of independently powered elementsindependently powered elements

Rs3

Xs1

Va

XC1

Xs3

IaI1

I3

XC3

Rs2

Rs4

Xs2

Vb

Xs4

IbI2

I4

XC4

kp

kp

kt

XC2

Rs1

kt

crit

Rs3

Xs1

Va

XC1

Xs3

IaI1

I3

XC3

Rs2

Rs4

Xs2

Vb

Xs4

IbI2

I4

XC4

kp

kp

kt

XC2

Rs1

kt

crit

EuratomTORE SUPRA


Effects of coupling on independently powered array elements

if the the array current pattern is not close to a “monopole” or “dipole” configuration

• Source/s) asymmetries are propagated by toroidal and (to less extent) diagonal coupling in both real and imaginary parts of the elements of both matrices and degenerate multiple eigenvalue solutions. As consequence, match acquisition becomes a four-parameter adjustment problem.

kt

0.01

0.023

0.037

0.05

0.1 0.2 0.3 0.4 0.50

20

40

60

80

Load resistance (Rs)

Cri

tical

pha

se a

ngle

kt 0.01kt 0.023

kt 0.037kt 0.005

Kt =0.010Kt =0.023

Kt =0.037Kt =0.05

Critical angle for a symmetric structure (X = 50 , R = 1 R0= 4 kp = 0.01)

• If source(s) asymmetries exceed a critical values (dependent on circuit power factor and coupling coefficients), the match is not possible with purely reactive components,

• This was the primary reason for the difficulties encountered in matching the TS profotype in vacuum.

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Functions of the ILS Trimmer

In case of large array coupling/ asymmetries, the pre-tuner input impedance is

Zin ~ (R0 + Rs +…) + i (Xsm+ Xs +….)

where the additional terms are load dependent.in a complicated way

In the most general case, the Trimmer is a two-reactance conventional tuning system operating wit time constant slower than the pre-tuner, so as to track its input impedance

For CD purposes depending on inter element couupling and plasma loading decouplers may be or not be needed

Isolators may be inserted at the input of the RF source, to make it operating at perfect match in any conditions.

Trimmer Decoupler

Decoupler

Isolator RF source

Main Transmission

Line

Source end

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Matching the ITER array

New layout

Reference design

Layout

Symmetric ILS

layout

Retracted first dielectric

VTL ceramic

supports

First vacuum containement

Remouvable VTL

Actuators

One of 12 module

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Electrical response of the tuning system

Electric field pattern at oerfect match (ideal ILS)

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Tuner EM response

Input reactance

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Current distribution in the bridge

Current probes

Voltage probe

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Vectorial admittance detector

V0 I1 I2

V0

C1

C2

I*k*I1

C2

L

I*k*I2

L

R

RL

V

V1

R

V2

Measured V1, V V2 Equivalent circuit

The three monitors have very close Thevenin impedances and distorsions in transmission are the same.

This makes vectorialmeasurements wideband

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Vectorial admittance detector

V1 V i k I1

V2 V i k I2

V0 V 1 2C2

C1

i k I1 I2

If R<< L<<1/C2

All ILS vectorial input parameters can be deduced by means of linear operations on V, V1 and V2.

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Array Integrated Control1. The overall array operation is controlled by independently acting in parallel on each ILS, with four

closed control loops, operating with equal time constants.

2. The four loops control are :1. The phase of the of the input currents to be 0 or toroidally and 0 poloidally ( toroidal “dipole”, poloidal

“monopole”

2. The input forward power to the value of P = 1/2R0 I2 by modulating the input forward voltage

3 &4 The admittances of all ILS half sections to be complex conjugate, by acting on asymmetry and average value of the tuning capacitors value and by applying the algorithms :

Re(Yin1) - Re(Yin2) = 0 and Im Yin1)+ Im(Yin2) = 0

3. The time constants of the fo ur loops should be selected in descending order.

4. Should a trimmer be necessary, the trimmer reactances should be operated by appying the perfect match algorithms

Re(in1) = 0 and Im in1) = 0

5. with time constant(s) equal for each ILS slower then the ones of th pre-tuner, so as the trimmer tracks the pre-tuner

6. Should be decoupler be necessary, they should be operated with time constant(s) equal for each ILS and slower than the ones of the trimmer

These combined controls will ensure within the time scale of the slowest loop : i) a load independent array k// spectrum; ii) full load resilience ,iii) a significantly decoupled operation of the array elements, stable control.

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Match acquisition in vacuum and on plasma1. Low power array electrical characterization

Prior to plasma operation the array elements need to be electrically characterized on a reproducible load (air and/ or vacuum) The low losses under this conditions ensure all control loops to operate at their maximum gain and possible servo instabilities can be readily detected.

The purpose of the electrical characterization is to establish reproducible initial conditions for the control loops.

It is desirable for the characterization to be performed using only monitoring equipment installed in the system and subsequently used on plasma operation, because this allows testing the overall system response The electrical characterization should be performed for all frequencies and array phase patterns used in operations

It is assumed that for each ILS the vectorial values of all input currents are measured

The input power should be regulated to a value low enough for the power source to accept 100% power reflection without damage and for the measurements to be performed with sufficient accuracy.

The phase between input currents should be regulated by feedback loops and using a single phase reference to the desired phase pattern This is assumed to be:

0 0

0 0

0 0

All control loops should operate

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STEP 1: ILS Characterization at no and vacuum radiation losses

1. Match without coupling• Each array elements should be shielded from the other ones by conductive walls. This is

obtained by covering the Faraday shield by a conductive metal sheet• Load resilience conditions should be applied and automatically obtained. The array should also

be perfectly matched. It should be noted that in this measurement load resilience is essentially lost because Rs << R0.

• The ILS no-radiation load (accounting for the copper losses in the resonant part of the circuit) can be deduced from the tuning capacitors calibration curves.

2. Measurement of poloidal coupling coefficient

• The shielding should be removed from one array element. Depending of the selected feedback condition, the tuning capacitors will adjust either to a mismatched input admittance.

• If the perfect match algorithm is applied the input admittance should adjust to a complex impedance from which the ILS internal coupling coefficient can be readily measured.

• If the optimum load resilience algorithm is applied, the input admittance should adjust to a real impedance differing from the nominal one by a small amount depending on coupling and load.

• The ILS vacuum radiation load (accounting for radiation and copper losses in the resonant part of the circuit) can be deduced from the tuning capacitors calibration curves.

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Step 2 : Array characterisation in vacuum

• When the array is inserted in the torus and commissioned in vacuum, the inter elements coupling coefficient may change slightly but, if the match condition in air is entered as initial condition, at power-up the control system will automatically re-match the array.

• The vacuum match patterns of the array for a certain frequency and array phasing should be memorized, to be re-entered as initial conditions for plasma operation.

1. Array characterization at no radiation losses

• With all control loops in operation under optimum load resilience condition, the shields covering the array elements should be sequentially removed from the center to the outside. After each removal there will be a re-arrangement of the tuning capacitors which will include the effects of toroidal and poloidal coupling and of array asymmetries.. For geometrically identical ILSs and a symmetric environment, the array matrix will have the pattern below below

A B B A

C D D C

A B B A

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Step 3. Plasma operationStep 3. Plasma operation

• When the array is applied to the plasma, the vacuum conditions should be imposed as initial conditions.

• At power up the array will automatic rematch and subsequently continuously adjust to slow plasma load variations plasma, whereas load variations are smeared out by load resilience.

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System protections

As all input admittances of the array are monitored at high frequency and controlled in closed loop, a sophisticated and selective array protection system can be designed by imposing vectorial operation windows to all array elements

A fast systematic real time monitoring of the loaded Q of each elements against closed loop values used as reference, will reveal pre – breakdown conditions.

Comparative real time monitoring loaded Q asymmetry within the same ILS(again against closed loop values ) provide indication of breakdown.

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Conclusions

• I trust we shall be able to give a demonstration of the method on the TS ITER Proto within 2005

This study demonstrates that:

• Controlling an array of ITER-like structures is not different from controlling an equivalent array of singlw straps

• Full load resilience can be automatically preserved by controlling all ILS currents to be conjugated with respects to the input currents

• Perfect match can be automatically acquired and reserved independent on inter-elements coupling and/or array or load asymmetries. If these are limited to reasonable values, two tuning elements/ ILS are sufficient. For large coupling and/or asymmetries a maximum of four may be required for plasma heating operations.

• Current drive operation is possible. Depending on plasma loading and inter elements coupling the use of decoupler may be necessary

• The use of isolators is always possible, with the added advantage that loads are resistive, decoupled and insensitive to load variations.

euratom tore supra g. bosia “matching iter-like structures” cadarache, 2-22 - 2005 matching...

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