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Transcript
```Euratom
TORE SUPRA
Matching ITER-like structures
G. Bosia
G. Bosia
“Matching ITER-like structures”
Euratom
TORE SUPRA
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.
The two secondary currents can be “reflected “ in the
primaries and the result is a N x N matrix problem of
the type :
ZL  I
V
where ZL is the so called “plasma impedance matrix”,
with elements describing array, plasma and vessel
electrical parameters, and including all couplings and
asymmetries .
The problem of matching the power sources ( Vk = R0 Ik)
leads to an eigenvalue problem of the type

ZL  R0
I
Rp
Mp
Rv
Xp
Mv
Xv
0
where R0 is a diagonal matrix.
G. Bosia
“Matching ITER-like structures”
Euratom
TORE SUPRA
Control of currents flow in a generic IC array

ZL  R0
I
0
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.
.
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
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
G. Bosia
“Matching ITER-like structures”
Euratom
TORE SUPRA
Control of currents flow in a generic array
The 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.
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
Single strap
In an array where the elements
are individually powered, the
strap current can be controlled
I
V
V = (Ls+ Lf) I
G. Bosia
“Matching ITER-like structures”
Euratom
TORE SUPRA
ICH untuned poloidal array elements
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.
dependent, and it is likely to be affected by local
dielectric properties of the “vacuum” at the first wall
V
V = (Ls+ Lf/2+ Lf/2) I
An untuned array is proposed also for ITER
V = (Ls+ Lf/3+ Lf/2) I
G. Bosia
“Matching ITER-like structures”
Euratom
TORE SUPRA
ICH tuned poloidal array elements
A good level of control of the poloidal currents is
possible in tuned poloidal arrays such as the
Resonant Double Loop (RDL)
V
Here the control of the reactive part of the current
is possible by making use of the tuning
capacitors.
V = (Ls+ Lf) I
In the ITER-like (ILS) structure, currents are
controlled to be complex conjugate, to
G. Bosia
“Matching ITER-like structures”
Euratom
TORE SUPRA
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
G. Bosia
“Matching ITER-like structures”
Euratom
TORE SUPRA
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.
G. Bosia
“Matching ITER-like structures”
Euratom
TORE SUPRA
What plasma impedance matrix should we expect in ITER?
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
We have for the moment only partial
•
•
.
In vacuum
On a “ dielectric” plasma
(eR = 200 + 200 i)
G. Bosia
“Matching ITER-like structures”
Euratom
TORE SUPRA
2X2 array impedance matrix in vacuum
G. Bosia
“Matching ITER-like structures”
Euratom
TORE SUPRA
2X2 array impedance matrix with dielectric plasma
G. Bosia
“Matching ITER-like structures”
Euratom
(As)symmetries of Z matrix induced by the
target medium : summary  
TORE SUPRA
•Antenna = 22 array, 4 identical poloidal straps.
•All symmetries verified with ICANT.
Vacuum =
dielectric with
toroidal B0
 Z11
Z
 12
 Z13

 Z14
Z12
Z11
Z14
Z13
Z13
Z14
Z11
Z12
Z14 
Z13 
Z12 

Z11 
4 independant
elements / 16
G. Bosia
Anisotropic
Dielectric,
tilted B0
 Z11
Z
 12
 Z13

 Z14
Z12
Z13
Z 22
Z 23
Z 23
Z 22
Z13
Z12
Z14 
Z13 
Z12 

Z11 
6 independant
elements / 16
Magnetized
plasma,
toroidal B0
 Z11
Z
 12
 Z 31

 Z 41
Z12
Z13
Z11
Z14
Z 41
Z11
Z 31
Z12
Z14 
Z13 
Z12 

Z11 
6 independant
elements / 16.
“Matching ITER-like structures”
 
Magnetized
plasma, tilted B0
 Z11
Z
 21
 Z 31

 Z 41
Z12
Z 22
Z 32
Z 31
Z13
Z 23
Z 22
Z 21
Z14 
Z13 
Z12 

Z11 
10 independant
elements / 16
Euratom
TORE SUPRA
Reduction of apparent interstrap coupling
•
0.2
0.02
0.1
0.01
S12 / S11 (full septum)
S12 / S1 (retracted septum)
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.
0
- 0.1
0.2
0
0.01
0.02
20
40
60
80
40
60
80
Frequency (MHz)
Frequency (MHz)
G. Bosia
20
“Matching ITER-like structures”
Euratom
TORE SUPRA
ITER-like structure : Simple (ITER Reference Design) case
 Rs  R0  i  X1  R0  i  X0.   I1 

  0

R

i

X
R

R

i

X
 s 0
0
2   I2 
  0
I1
R0 + i X0
X2
I2
Xs2  X0  XC2
X0
 Rs  R0  i   Xs1  Xsm  XC1

R0

1
XCM
2
XCM
XM

XCM
XCM
0
  I1 
  0
 Rs2  R0  i   Xs2  Xsm  XC2   I2 
R0

 XC1  XC2
1
2

I1M

 XC1  XC2
0
XM
G. Bosia
X2
X1
R2
Xs1  X0  XC1
X1
R1
I2M

Rs  2  R0  Rs
Xs  XM

Iin
V

Rs  i  Rs  2  R0  Rs
V



Rs  i  Rs  2  R0  Rs 
V
R0
Xs  XM
“Matching ITER-like structures”
Euratom
TORE SUPRA
An “ideal” ITER-like structure is resilient to load variations if it is matched to an input resistance R0
typically 5 times the load resistance Rs
2
Z1 = Rs1+1i Xs1
XC1
Z0 = R0+1i X0
XC2
Z2 = Rs2+1i Xs2
Voltage standing rwave ratio
RM
XM
R0= 30 
0
S max
1.75
1
R0= 22 
R0= 14 
1.5
.
S max
1.25
1
1.35
0
R0= 6 
2.69
4.03
5.36
6.7
It was suggested 1) that the load resilience would be impaired by the inductive coupling between straps.
1)
G. Bosia
A. Messsiaen, 15th Topical Conference on Power Application to Plasmas (2003)
“Matching ITER-like structures”
Euratom
TORE SUPRA
ITER-like structure : General case
I1
Rm1+i Xm1
 R 1  1i  X 1 R m2  1i  X m2   I 1 

  0
 R m1  1i  X m1 R 2  1i  X 2   I 2 
R1
X1
R0 + i X0
Rm2+i Xm2
Rk
Rsk  R0
Xk
Xsk  X0  XCk
R2
Rmk
Rsm2  R0
Xmk
Xsm1  X0
X2
I2
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 
G. Bosia
X0 ~ 0 
Rs< 1 
Xs ~ 20 
Rsm< Rs<< R0
Xsm< Xs
Rsk< Rs<< R0 Xsk<< Xs
Rsm< Rs<< R0
Xsm<< Xsmk
“Matching ITER-like structures”
but not << X0
Euratom
TORE SUPRA
ITER-like structure: General case (approximate)
Rs << R0 , Rsm << R0 ,
If
Xs << Xs , Xsm < Xs but not << X0
  Rs  R0  i  X1 R0  i   X0  Xsm   I1 

  0

R

i

X

X
R

R

i

X




0
sm 
s2
0
2   I2 
  0
Rs
1
2


 Rs1  Rs2
1
Rs
2
Xsm  X0
 Rs  R0  i   Xs1  Xsm  XC1

R0

XCM
 Xs  Xsm  XM
XCM
XCM
Rs
G. Bosia
Xs  XM
1
2
1
2


I1M
V
R0  i  Xsm
V
R0  i  Xsm


Xs1  X0  XC1
X2
Xs2  X0  XC2
  I1 
  0
R

R

i

X

X

X
 s2 0  s2 sm C2   I2 
 XC1  XC2

0
X1
R0
I2M
 XC1  XC22

 Rs1  Rs2
Iin


R0

Rs  i  Rs  2  R0  Rs
R0



Rs  i  Rs  2  R0  Rs 
V
R0  i  Xsm
“Matching ITER-like structures”
Euratom
TORE SUPRA
Conclusions on matching a single ILS
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).
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.
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.
G. Bosia
“Matching ITER-like structures”
Euratom
TORE SUPRA
Preserving load resilience by control of the ILS currents
The 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:
XC
XC

 
Xs  Xsm  tan ( f)  Rs  Rsm

Xs  Rs
 Rs  Xsm   Rsm  Rs
tan ( f)
 Rs  Xsm   Rs  Rsm
R0 cos ( f)   Rs  Rsm  sin ( f)   Xs  XC  Xsm
where Rs, Xs, Rsm, Xsm XC, and  Rs,  Xs,  Rsm,  Xsm  XC are arithmetic averages and
asymmetries of the matrix elements, f is the 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
G. Bosia
“Matching ITER-like structures”
Euratom
TORE SUPRA
Generic layout of a tuned ILS
Main
Transmission
Line
Decoupler
Trimmer
Pretuner
Isolator
ILS
G. Bosia
“Matching ITER-like structures”
RF source
Decoupler
Source end
Euratom
TORE SUPRA
Functions of the Pre-tuner
•
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
Re(I1/Iin)- Re(I2/Iin)=0
and
Im(I1/Iin)+Im(I2/Iin)=0
or equivalently
•
The conjugate angle is load dependent and it increases with the load power factor. This conditions
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)
.•
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
G. Bosia
“Matching ITER-like structures”
Euratom
TORE SUPRA
Functions of the ILS Pretuner
•
For higher coupling coefficients and asymmetries, the mismatch is eliminated by a two reactance trimmer
•
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.
43.8
|I1|- |I2| = 0
kp = 0.0
43.8
|I1|- |I2| = 0
C2
pF 42
C2
pF42
40
40
38.8
38.8
38
38
36
36
34
33.8
(Arg(I1) - Arg(Iin) + (Arg(I2) - Arg(Iin) = 0
(Arg(I1) - Arg(Iin) + (Arg(I2) - Arg(Iin) = 0
34
m33.8
G. Bosia
kp = 0.04
36
38
34
40
38.8
42
C 1 (pF) 43.8
33.8
34
33.8
m
“Matching ITER-like structures”
36
38
38.8
40
42
C 1 (pF) 43.8
Euratom
TORE SUPRA
Coupling effects on networks of
independently powered elements
• 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.
F>F
F<Fcrit
crit
XXC1
C1
II11
IaI
XXC2
C2
a
I2I
VVa
a
RRs1
s1
kkt
t
XXs1
s1
IbI
VVb
b
RRs2
s2
kkp
p
b
2
XXs2
s2
XXs3
s3
kkt
t
kkpp
XXs4
s4
RRs3
s3
XXC3
C3
I3I
3
RRs4
s4
I4I
4
XXC4
C4
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)
G. Bosia
“Matching ITER-like structures”
Euratom
TORE 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.
 0.01 
0.023 
kt  
Critical angle for a symmetric structure 0.037 
(X = 50 , R = 1, R0= 4, kp = 0.01) 0.05 
• 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,
Critical phase angle
• This was the primary reason for the
difficulties encountered in matching the TS
profotype in vacuum.
80
60
40
Kt =0.010
kt
20
0
0.1
G. Bosia
“Matching ITER-like structures”
0.2
0.01
=0.023
kK
t t 0.023
0.3
Kt =0.037
kt
0.037
kt K0.005
t =0.05
0.4
0.5
Euratom
TORE SUPRA
Functions of the ILS Trimmer
In case of large array coupling/ asymmetries, the pre-tuner
input impedance is
Zin ~ (R0 +  Rs +…) + i (Xsm+  Xs +….)
complicated way
Main
Transmission
Line
Decoupler
Trimmer
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
Isolator
Decoupler
Source end
Isolators may be inserted at the input of the RF source, to
make it operating at perfect match in any conditions.
G. Bosia
“Matching ITER-like structures”
RF source
Euratom
TORE SUPRA
Matching the ITER array
One of 12 module
New layout
Symmetric ILS
layout
Retracted first
dielectric
First vacuum
containement
Actuators
Reference design
Layout
VTL ceramic
supports
G. Bosia
Remouvable VTL
“Matching ITER-like structures”
Euratom
TORE SUPRA
Electrical response of the tuning system
Electric field pattern at oerfect match (ideal ILS)
G. Bosia
“Matching ITER-like structures”
Euratom
TORE SUPRA
Tuner EM response
Input reactance
G. Bosia
“Matching ITER-like structures”
Euratom
TORE SUPRA
Current distribution in the bridge
Current probes
Voltage probe
G. Bosia
“Matching ITER-like structures”
Euratom
TORE SUPRA
C1
V0
I1
V
I*k*I2
I*k*I1
I2
V1
V0
L
L
R
R
C2
C2
V2
RL
Equivalent circuit
Measured
V1,
V
V2
The three monitors have very close Thevenin
impedances and distorsions in transmission
are the same.
This makes vectorialmeasurements wideband
G. Bosia
“Matching ITER-like structures”
Euratom
TORE SUPRA
If
R<< L<<1/C2
V1
V  i    k  I1
V2
V  i    k  I2
C2 

V  1  2 
  i    k  I1  I2
C1 

V0


All ILS vectorial input parameters can be deduced by means of linear operations
on V, V1 and V2.
G. Bosia
“Matching ITER-like structures”
Euratom
TORE SUPRA
Array Integrated Control
1.
The overall array operation is controlled by independently acting in parallel on each ILS, with four
closed control loops, operating with equal time constants.
The four loops control are :
2.
The phase of the of the input currents to be 0 or p 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 :
1.
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.
G. Bosia
“Matching ITER-like structures”
Euratom
TORE SUPRA
Match acquisition in vacuum and on plasma
1.
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
p
0
p
0
p
0
p
0
p
0
p
All control loops should operate
G. Bosia
“Matching ITER-like structures”
Euratom
TORE SUPRA
STEP 1: ILS Characterization at no and vacuum
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.
•
impedance differing from the nominal one by a small amount depending on coupling and load.
•
the circuit) can be deduced from the tuning capacitors calibration curves.
G. Bosia
“Matching ITER-like structures”
Euratom
TORE SUPRA
Step 2 : Array characterisation in vacuum
•
•
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
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.
G. Bosia
“Matching ITER-like structures”
Euratom
TORE SUPRA
Step 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
G. Bosia
“Matching ITER-like structures”
Euratom
TORE SUPRA
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.
G. Bosia
“Matching ITER-like structures”
Euratom
TORE SUPRA
Conclusions
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
•