A magnetically driven reciprocating probe for tokamak scrape-off layer
measurements
J. P. Gunn and J. -Y. Pascal
CEA, IRFM, F-13108 Saint-Paul-Lez-Durance, France.
ABSTRACT
A new in-situ reciprocating probe system has been developed to provide scrape-off layer measurements
in the Tore Supra tokamak. The probe motion is provided by the rotation of an energized coil in the
tokamak magnetic field. Simple analytic approximations to the exact numerical model were used to
identify the important parameters that govern the dynamics of the system, and optimize the coil
geometry, the electrical circuit, and the stiffness of the retaining spring. The linear speed of the probe is
directly proportional to the current induced by the coil's rotation; its integral gives the coil position,
providing a means to implement real-time feedback control of the probe motion. Two probes were
recently mounted on a movable outboard antenna protection limiter in Tore Supra and provided
automatic measurements during the 2011 experimental campaign.
I. Background
The torque exerted by the tokamak magnetic field on an energized solenoid was first used to
move Langmuir probes in ASDEX-Upgrade [1]. Langmuir probe tips were mounted at the end of a
long arm, which swang into the divertor plasma. The probe excursion, projected onto the tokamak
major radius, was about 20 cm long. A similar swinging probe was installed in RFX with a 5 cm radial
excursion [2]. A tiny version was used in Alcator C-Mod on the inboard wall of the tokamak [3],
providing radial excursions of about 1 cm.
The problem with a swinging arm is that the probe collectors change orientation with respect to
the magnetic field during the movement, complicating the data analysis due to the variation of effective
collecting area. In the Tore Supra tokamak [4], tunnel probes [5] are preferred, which must remain
aligned with the magnetic field at all times, so we cannot adopt the swinging arm concept. Recently in
Alcator C-Mod, based on the same principle that was used to open and close "Venetian blinds" to vary
divertor bypass geometry [6], a magnetically driven probe was developed with fixed orientation of the
tips. The probe head is mounted on a stage that can move 1.7 cm radially [7]. The stage is displaced by
four legs that swing together, and between two of which a coil is fixed. To produce radial excursions of
5 cm, such a system would necessarily occupy a lot of space when retracted, and must be placed near
the plasma, causing concern about heating during high power, steady state discharges. Therefore, the
system designed for Tore Supra closely follows that of the ASDEX filament probe [8], which uses the
leverage provided by a coil rotation to produce a linear movement. Two coil drive assemblies are
attached to the rear side of the mobile antenna protection limiter (APL) in Tore Supra where significant
port volume is available, hidden from the plasma. Each of the cylindrical probe heads moves radially
through a 22 mm diameter hole into the scrape-off layer. We call this probe the "pecker probe" since it
reminds us of a woodpecker pecking on a tree trunk.
The purpose of the ASDEX filament probe is to measure particle flux in ELM filaments that
propagate across the last closed flux surface (LCFS) towards the first wall. The procedure to move the
probe is well illustrated in Fig. 7 of Ref. [8]. Upon application of a positive voltage to the coil, the
probe quickly advances to its maximum position. The voltage is maintained for 2 s, then turned off,
after which a spring retracts the probe to its rest position. The scenario in Tore Supra is different. The
probe must measure very close to and even inside the LCFS, so the total duration of its excursion must
be kept as small as possible to avoid overheating and damage. The probe is never held immobile in the
plasma, but must move constantly. Ideally, the trajectory of the pecker probes should be similar to
those of the existing reciprocating probes [9], lasting about 100 ms, with maximum speeds around 1
m/s, and this independent of the magnetic field strength. When the probe attains a pre-defined position
slightly before reaching the inner hard stop, the applied voltage is changed in order to reverse the
applied torque. These constraints implied that we had to model the fast entry phase of the probe in
order to dimension the coil to work for the full range of magnetic field in Tore Supra, and furthermore,
that real time feedback on the probe position would be necessary in order to control the coil voltage.
The probe drive and the model of its motion are described in Section II. Because we mounted
the probes directly in the tokamak without testing them in a strong magnetic field, we had to leave a
margin for uncertainties due to the influence of eddy currents on the dynamics. In Section III some
simple estimates of eddy currents are given. Section IV concerns exact numerical solution of the model
which was used to develop the real-time feedback algorithm for controlling the probe reciprocations,
outlined in Section V. In Section VI some examples of real measurements demonstrate the good overall
performance of the system, conform with the design predictions.
II. Dynamical model
A photograph of the drive mechanism and a schematic illustrating the geometry are shown in
Figures 1 and 2 respectively. The rotating coil provides leverage which is converted to linear motion of
the probe via wheel bearings. The probe shaft was treated with a diamond-like coating to reduce sliding
friction under vacuum. The maximum angular rotation (50°) of the coil and the length of the lever arm
(54 mm) give a linear probe excursion of 46 mm along the tokamak minor radius. This excursion is
limited by pins in the fixed support. In order to reduce hard shocks when striking these pins, a 0.8 mm
thick tempered stainless steel blade was attached to the stirrup to cushion impacts. When in motion
between the inner and outer hard stops, the stirrup is electrically insulated from the grounded support
by the ceramic wheel bearings, and the diamond coating on the probe shaft. To prevent electrical
contact via the retaining spring its fixation point upon the grounded support was isolated using mica
sheets. Applying a small voltage between the stirrup and tokamak ground creates a contact circuit;
current flows only when the flexible blade touches either of the two pins, providing a redundant means
to detect whether the probe is correctly docked when not in use.
The angular acceleration of the coil is governed by four torques produced by: (1) the magnetic
moment of the drive coil current, (2) eddy currents in moving parts, (3) the retaining spring, and (4) the
opposing inertia of the probe head. Friction is neglected. The appropriate dynamical equation is
 ̈=coil eddy  spring  probe
(1)
where ι=3.2×10-4 kg m2 is the moment of inertia of the coil plus the stirrup to which it is bolted.
The rotational axis of the coil is tilted 5° away from the poloidal direction so that on average the
system will fully exploit the torque produced by both poloidal and toroidal components of the magnetic
field. Upon application of a voltage V, the torque coil = B cos  causes the coil to rotate to align the
magnetic moment =N I A with the total magnetic field B. The coil is characterized by the number of
windings N each having cross section A. As the coil rotates, an electromotive force (back emf) is
generated due to the variation of magnetic flux through the windings, modifying the current I in the
drive circuit with respect to the purely ohmic value
1
d
dI
I = V −N B A sin −L self
(2)
R
dt
dt


where R is the total electrical resistance of the circuit and
L self =0 N 2 A/h
(3)
is the self inductance of the coil. The angular velocity of the coil, obtained from measurements of the
coil current and applied voltage, is integrated to yield the probe position. The length of the coil is h.
With Lself~mH and R~Ω, the inductive time constant of the drive circuit is around 1 ms. Since the
duration of the probe reciprocation will be around 100 ms, the self inductance can be neglected. Doing
so introduces a small error on the position measurement, which will be evaluated numerically in
Section 4. For the purposes of the present qualitative analysis, we drop the self inductance term from
the magnetic moment.
From Eq. (2) it is apparent that the coil torque can be written as the sum of two torques, one due
to the applied voltage, appl , independent of the coil's motion, and the second due to the back emf,
emf :
coil =appl  emf =
N A B cos
 N A B cos 2
V−
̇ .
R
R
(4)
The second term is akin to viscous drag. Any movement of the coil can be seen as inducing a current
that produces a torque to oppose the rotation. When the coil rotates towards the field at the beginning
of the reciprocation, a counter current is induced, reducing the torque below that which would be felt
by an immobile coil. On the return phase of the reciprocation when the coil is rotating back to its rest
position, the induced current produces a torque that resists the spring, making it more difficult to retract
the probe.
In the same way that the back emf induced by the coil's rotation damps its motion, eddy currents
generated in the moving components of the probe and support structure will increase the sluggishness
of the system. It is possible to make simple estimates of eddy currents, without having to resort to
calculating them in conductors of complex shape, which is a formidable problem of electromagnetics.
Just like emf , eddy is always proportional to the angular velocity of the coil, so for convenience we
shall simply express it as being due to the back emf in a second, unbiased copper coil of the same
geometry as the drive coil, with a number of windings Neddy :
− N eddy A B cos 2
eddy =
̇
R
(5)
where we implicitly assume that the eddy current loops have the same orientation with respect to B as
the coil. This approximate formulation is useful because it gives an indication of the relative
importance of eddy currents in the conducting support with respect to the counter currents induced in
the coil. For concreteness some simple estimates of eddy currents are listed in Section 3, where it shall
be shown that we can minimize their effect, depending on the probe design.
To simplify the model, we assume a spiral retaining spring that exerts a torque proportional to
its angular displacement away from equilibrium
 spring =−k  −0 
(6)
where k is the spring constant and θ0< θmin is the angle for which the spring is relaxed; it is always
under tension in order to keep the probe retracted when no current is applied to the coil. The final
design incorporates a linear tension coil spring attached to the stirrup (cf Figure 1), but the force curve
as a function of drive coil angle can be reasonably well fit by Eq. (6).
Finally, the inertia of the probe head itself exerts a torque
 probe =−l m ẍ cos
(7)
where m=0.25 kg is the estimated mass of the probe head, l=54 mm is the lever arm between the
stirrup's rotational axis and the wheel bearing that exerts force upon the probe body, and
x=l sin −sin  min 
(8)
is the linear probe displacement along the tokamak minor radius.
Combining all these torques, Eq. (1) describing the coil rotation becomes
 ̈=
 B Acos  2
R
[
]
2
NV
− N 2 N 2eddy  ̇ −k  −0  −l 2 m [ ̈cos 2 − ̇  sin cos ]
B A cos 
(9)
Before solving Eq. (9) equation numerically in Section IV, the basic dynamical properties of the
pecker probe can be anticipated analytically. Eq. (9) reduces to a linear differential equation under the
approximation of small angular rotations
 l2 m  ̈= B A NV − N 2N 2eddy  B A ̇ −k  −0  .
(10)
R
[
]
It is instructive use Eq. (10) to analyze the motion of the pecker probe operating in an ASDEXlike scenario. The procedure described in Ref. 8 is to apply a positive voltage to the coil to drive the
probe into the plasma, hold it there for 2 s, then set the voltage to zero to allow the spring to retract the
probe. In the absence of a magnetic field, the natural oscillation frequency of the system is
=

k
l 2 m

.
(11)
For example, if the coil were manually rotated to its maximum position =max and then released, the
spring would pull it back to its rest position in around 65 ms, assuming total inertia around 10-3 kg m2,
and spring constant k=0.35 Nm/rad. The angles are set to max=25° ,  min =−25° , and 0=−50° . If
the same excercise is made in the presence of the magnetic field, the torque emf exerted by the back
emf can dominate the spring force especially if the number of windings is large. Therefore, if we
wanted to use the spring to retract the probe quickly, we would need to minimize the number of
windings. We can get a rough idea of the maximum number of windings by identifying the critical
condition for which the solutions of Eq. (10) change from underdamped to overdamped, that is,
dominated by the spring or dominated by the back emf and/or eddy currents:
 N 2N 2eddy 
2
2
2
 B A
4 R  l m 
4
k
(12)
Neglecting eddy currents, we find N ≈56 for typical parameters (B=3 T, A=0.002 m2, R=3 Ω). If eddy
currents produce significant torque (e.g. Neddy>56), the system will always be overdamped, independent
of the number of windings in the drive coil.
As seen in Fig. 7 of [8] it was reported that the ASDEX filament probe returns very slowly to its
rest position. According to Eq. (12) the free motion of that coil, with its 266 windings, is dominated by
the back emf, even neglecting eddy currents. The observed behaviour is well reproduced by numerical
solutions of Eq. (9) comparing the undriven movements of coils with 56 and 266 windings, with and
without magnetic field (Figure 3). With magnetic field, both coils become more sluggish, but clearly
the rotation of the ASDEX-like coil is much more strongly damped.
It was suggested [8] that the return velocity could be increased either by using a stiffer spring,
or by applying a negative voltage to the coil. The former option would not work, because according to
Eq. (12) the free motion is nearly independent of the spring constant when the number of windings is
large. This is illustrated in Figure 4 where the retraction time is plotted as a function of the number of
windings for two different spring constants, with and without an applied negative voltage. Even with a
spring constant k=3.5 Nm/rad, i.e. ten times the stiffness of the spring we use, the ASDEX-like coil
takes about 300 ms to retract without the help of a negative drive voltage.
If an extremely stiff spring were used to retract the probe without the assistance of a negative
voltage, it would be difficult to insert the probe because the applied torque would be insufficient. From
Eq. (9) the maximum spring constant for which the probe can be maintained in equilibrium at its
deepest position can be determined as a function of the number of coil windings. The power supplies
we use can deliver 36 V / 12 A, which is insufficient to provide enough torque. We conclude that the
spring should not be especially stiff. Both the forward and backward motions of the probe must be
controlled by the applied voltage. The only direct function of the spring is to keep the probe retracted
behind the limiter tiles between reciprocations.
Three criteria imposed by hardware performance determine the number of windings and the
voltage needed :
1) To provide a margin for error, we allow at most 20 V applied voltage, knowing that the power
supply can deliver 36 V.
2) The minimum voltage Vmin for a given number of windings is determined by the requirement that the
coil be able to provide sufficient torque to overcome the spring force. To determine this minimum
voltage we choose the angle of equilibrium  eq for which the applied torque balances the spring force
to be well beyond the maximum angle, for example eq=2 max . In steady state, Eq. (9) gives
R k   eq−0 
V min=
.
(13)
N B A cos eq
3) Numerous numerical trials varying the number of windings taught us that it would be tricky to damp
the return motion of the probe and bring it gently to rest by means of active feedback of the voltage
waveform. It was therefore desirable to choose a sufficient number of windings such that the system
operates in the overdamped regime so that the induced currents provide significant damping when
needed. A robust procedure appears to be to apply a positive voltage to insert the probe, reverse it when
the probe approaches its target depth, allow it to return towards its resting position, and finally turn off
the voltage at a critical position so that magnetic braking takes over and lets the probe settle gently into
place behind the APL tiles. The minimum effective number of windings is given by Eq. (12).
The optimal voltage Vopt for a given number of windings is determined as follows. Typically, we
want the system to operate in a saturated regime in which the retaining spring plus the induced currents
in the coil and in the moving components of the drive mechanism nearly cancel the torque produced by
the applied voltage; the coil rotates with its terminal angular velocity. We impose a value deemed
necessary to prevent overheating of the probe by plasma irradiation

̇ term=
(14)
 t in
where  =max−min and  t in is the duration of the inward motion. Setting the angular acceleration
to zero in Eq. (10), we obtain the approximate value of the appropriate voltage
V opt
N 2N 2eddy  B A   R k 0

=
−
N  t in
N BA
.
(15)
Both Vopt and the number of windings must satisfy the three restrictions listed above. It should be noted
that most plasma scenarios use the maximum magnetic field in Tore Supra, B=3 T at the outboard
midplane. However, some scenarios use as little as half that value, in which case it is possible that a
small number of windings might be insufficient to dominate the spring force if this number were
optimized for full field operation. Furthermore, the system might be in the underdamped regime at low
field. Therefore, a pragmatic approach is to optimize the coil for low magnetic field operation, and
adjust the voltage waveform as necessary for high field operation. The range of allowable coil windings
and applied voltages are delineated in Figure 5. Neglecting eddy currents, the number of windings
should be chosen between 110 and 180 in order to guarantee system performance over the full range of
magnetic field used in Tore Supra.
Eddy currents increase the magnetic braking of the device and decrease the probe velocity for a
given applied voltage. In order to maintain coil performance in the presence of significant eddy
currents, the applied voltage must be increased. In the next section we shall make simple estimates of
eddy currents and evaluate their effect.
III. Estimation of eddy currents
For an eddy current to flow in a closed loop inside a moving conductor there must be a time
varying magnetic flux through its cross section. This can occur if a component of the object's velocity
is parallel to the gradient of a spatially non-uniform magnetic field, or if it rotates about an axis that is
not parallel to a magnetic field. As a reference, let us cite the divertor bypass flaps that were
implemented in the Alcator C-Mod tokamak [6]. These were a set of rectangular inconel plates whose
axis of rotation was oriented along the tokamak major radius. While rotating due to the torque provided
by an energized 60-turn coil, a flap presents a variable cross section as viewed along the toroidal
magnetic field. The torque produced by the resulting eddy current loop is
eddy =−  B 2 cos 2  ̇
(16)
where κ is a constant dependent on the properties of the flaps. Setting this equal to Eq. (5) gives the
equivalent number of windings of a hypothetical drive coil of the same geometry as the one that was
installed (cross section A≈10−3 m 2 )
R
N eddy = 
(17)
A
which gives N eddy ≈74 for the Alcator case ( =8×10−4 m4 −1 , R=6.8 Ω). Eddy currents produce
50% more torque than the back emf. As concluded in [6], "the main resistance to opening is the eddy
current induced in the flap as it rotates through the strong toroidal magnetic field."
In the case of the pecker probe, the coil support, or "stirrup", rotates, but most of its surfaces are
parallel to the magnetic field, so there is little variation of magnetic flux. The only part which intersects
the field at an appreciable angle is the flat bar (the "tread" to which the coil is attached) joining the two
sides of the stirrup together (Figure 6). Apart from being twice as thick, its dimensions are nearly the
same as the bypass flaps in Alcator C-Mod, so the eddy currents circulating in it are nearly twice as
large (see Eq. 5 of [6]). However, the effective area of the coil in Alcator C-Mod was around NA=0.05
m2, whereas in Tore Supra it is larger, NA=0.25 m2. Depending on the value of circuit resistance (a
range of 2-4 Ω was assumed during the design phase of the project), we find estimates 27N eddy 38
e.g. the eddy current torque would be 3% to 6% of the torque produced by the back emf in a 160-turn
coil. Such values do not significantly modify the behaviour of the system (Figure 5) and can be safely
ignored.
A prototype drive mechanism, built to test the performance of the sliding contacts and wheel
bearings under vacuum without magnetic field, included a support rod to which the retaining spring
was attached. This rod connected the two sides of one extremity of the stirrup and would provide a path
for around 200 A of eddy current to flow, closing a loop through the tread. An estimate of the resulting
torque leads to
2
2
−l L A B cos
eddy ≈ rod rod rod
̇
S.S.
(18)
where lrod is the lever arm of the spring support rod, Lrod and Arod are its length and cross section
respectively, and  S.S =7.4×10−7  m is the electrical resistivity of stainless steel. This is the same
torque as would be induced by the back emf in a coil having N eddy =93 windings. If the support rod had
been included in the final design, the eddy current would have exerted nearly half the torque as that
produced by the back emf in a 160-turn coil.
Strong eddy currents impose a reduction of the number of coil windings and an increase of the
applied voltage to maintain the desired reciprocation speed. It is important to note that the total
magnetic moment of the system, and the terminal rotational velocity, are given by the sum of the
current in the rotating coil (multiplied by the number of windings) and the eddy current in the stirrup.
To force the coil to rotate at a particular value of terminal velocity, when all the torques are in
equilibrium, the power supply must deliver a curent of roughly
N 2eddy B A  
k 0
I eq=
−
.
N R  t in
NBA
(19)
It is clearly of interest to eliminate large current loops in the moving parts of the probe drive such that
most of the counter torque is produced by the coil. If this can be achieved, then the total coil current is
minimized, which reduces resistive heating of the copper wire. Therefore, we decided to suppress this
rod from the final design.
Simple analysis allowed us to identify the main features of the pecker probe dynamics that
guided our choice of hardware solutions. The numbers obtained are only approximate. In the next
section, a more refined numerical study will be described.
IV. Detailed numerical simulations
Next we needed to optimize the coil geometry respecting hardware limits and leaving some
margin for error. Until now, we have been using typical values of the parameters in order get an idea of
the dimensionality of the problem. For example, we used constant circuit resistance, but in fact, that
depends on the number of windings and on the diameter of the copper wire. In the analysis that follows,
Eq. (9) has been modelled numerically, including consistent values of circuit resistance, coil inertia,
and coil area (that is, taking into account the number of layers of cable needed to wind the coil). The
moment of inertia of the coil and its electrical resistance depend on the length of the cable needed to
make N windings. We assume copper wire with a 50 µm thick insulating coating. The coil support is
made of Vespel and weighs about 60 g, and the probe head itself is assumed to weigh 0.25 kg. The self
inductance of the coil is included in the calculation [cf Eq. (2)].
Simulations were run for a broad range of winding numbers at low and high magnetic fields,
and for three eddy current values. The optimized applied voltage Vopt is shown in Figure 7a. Moderate
eddy current (Neddy=40) imposes the use of voltages above 20 V, but which are nonetheless within the
output range of the power supply (36 V). Only if eddy currents are much higher than estimated would a
large number of windings be a problem. The net current in the drive circuit during the constant-velocity
entry phase [Eq.(19)] is shown in Figure 7b. For moderate eddy currents the drive circuit current
remains quite low in all cases. Based on these results, we decided to incorporate four layers of 40
windings each into the coil.
The response of an optimized system with N=160 at full field is shown in Figure 8. An insertion
time  t in =50 ms was imposed. The optimal voltage Vopt=18.8 V. With 26.3 m of 1 mm diameter
copper wire, the coil resistance is R=0.8 Ω. The total resistance of the 50 m cables that carry the current
from the coil to the power supply, plus the 0.10 Ω shunt resistor and contact resistances, is 1.35 Ω. The
self inductance of the coil is L=1.6 mH. Curves of (a) probe position [cf Eqs.(20-22) below], (b) probe
speed, (c) probe acceleration, and (d) coil current (along with its three components, cf. Eq.(2)) were
calculated. The transition times of the applied voltage waveform were chosen to keep the acceleration
below 100 m/s2.
V. Real time position control
During a probe reciprocation measurements of the applied voltage V at the output of the power
supply and the net current I in the drive circuit are acquired every 1024 µs. Neglecting self inductance,
Eq. (2) defines the current induced by the coil's rotation as
V
NBA d
I ind =I − =−
sin  .
(20)
R
R dt
In order to guarantee that self inductance can be neglected, we avoid sudden changes of the applied
voltage (that is, on a millisecond time scale), as will be described below. The magnetic field B at the
probe position is deduced from magnetic measurements and the instantaneous position of the APL that
are broadcast in real time over the reflected memory network of Tore Supra [10]. The drive circuit
resistance R varies with ambient temperature. At the nominal tokamak baking temperature T=400 K,
the electrical resistivity of copper is 2.4×10-8 Ωm and it increases by 2.8% for a temperature increase of
10 K. The total drive circuit resistance is measured by briefly applying a small negative voltage to the
coil before each reciprocation and dividing it by the resulting current. This also serves to fully retract
the probe behind the APL tiles in case it is not there already, to ensure the same starting position (x=0)
for every reciprocation.
The linear probe speed [cf Eq. (8) and Figure 2] is
d
v =l sin .
(21)
dt
Comparing with Eq. (20) we see that the probe speed is directly proportional to the induced current
lR
l
v =−
I ind =
 V −RI  .
(22)
NBA
NBA
The instantaneous probe position is obtained by integrating this equation starting from the beginning of
the reciprocation.
Before each discharge, the probe operator stores a list of times treciprocation at which each
reciprocation is to begin. Each probe reciprocation is divided into five phases.
Phase 1 starting at t=t1<treciprocation: Determination of digitial offsets to be subtracted from drive voltage
and current measurements. This phase lasts 50 ms.
Phase 2 starting at t=t2 <treciprocation: Measurement of drive circuit resistance by applying a small negative
voltage to the coil. This phase lasts 100 ms.
Phase 3 starting at t=treciprocation : Fast insertion. Attaining a specific speed depends on parameters that are
difficult to predict, such as eddy currents [Eq. (15)], so the applied voltage is controlled by feedback on
the measured speed using a proportional-integral (PI) gain algorithm. At each instant the probe speed is
compared with the target speed waveform vt. The difference between the two
=v t −v
(23)
is used to determine the new drive voltage

t
V =K p 
1
∫ d 
 int t
3

(24)
where Kp is the proportional gain and τint is the characteristic time it takes the integral term to cancel
errors. The inertial time response of the mechanical system to a voltage pulse defines the minimum
integration time that can be effectively used by the feedback routine. From the solution of Eq. (10) in
the strongly overdamped regime we obtain the estimate
int 
R  l 2 m
 N 2 N 2eddy  B2 A 2
.
(25)
The design parameters of the probe predict τint=1 ms and 6.5 ms for B=3T and 1.5 T, respectively. In
practice, due to the delay between measurement and correction of the applied voltage, we found that
τint=2.5 ms is a good compromise for all fields. Both numerical simulations and tests without plasma
show that Kp=5 gives good results.
The probe speed is ramped from 0 to vmax (usually 1 m/s) during a time interval
 t start=v max /amax in order to keep the acceleration below a max =100 m/s2. Then the target speed of vmax
is maintained until a pre-defined critical position x 3=x t− x is reached. The target position xt is
specified by the operator in terms of an absolute distance from the resting position. For safety, a
minimum distance of approach relative to the LCFS can also be defined, and supercedes x t if
necessary. The position of the LCFS is calculated in real time based on magnetic flux measurements.
The next phase of the reciprocation is triggered when the probe arrives at the first of those two
positions, minus a small offset  x , described below, to account for inertia.
Phase 4 starting at t=t4 : Fast retraction phase. Towards the end of Phase 3 (fast insertion), the feedback
routine has found the optimal voltage Vopt needed to move the probe with the desired speed vmax. Once
the critical position x 3 is crossed, the feedback routine is halted and thereafter predefined voltage
waveforms are applied. The voltage is reversed during  t switch =4  x / v max in order to start bringing
the probe back towards the LPA at speed -vmax. During half of this time, the probe will advance to the
ultimate target position before reversing direction. Then the voltage is maintained at V=-Vopt. The
control program continually estimates the time needed to halt the motion, determined by the
instantaneous probe speed and the maximum allowed acceleration. When the probe reaches a certain
position x 4 near the end of its trajectory, the final phase of the reciprocation is triggered.
Phase 5 starting at t=t5 : Slow docking phase. To avoid slamming the probe violently onto the outer
hard stop, the voltage is ramped down to gently immobilize the probe at a position x 5 , just behind the
CFC tiles, but still 1 or 2 mm in front of the resting position x=0. We want the position to vary like
t−t f 2
x=x 5 x 4−x 5 
(26)
t f −t 5 2
The time needed to decrease the speed to be zero exactly when the probe arrives at position x5 is
determined by the speed v4 measured at time t5 and the maximum allowed acceleration:
v4
t f −t 5=
(27)
a max.
Finally, at tf the applied voltage is shut off and the probe, whose speed is limited by the back
emf, is drawn gently to its resting position by the retaining spring.
VI. Performance
Two probes were attached to the rear face of the APL at poloidal angles =±19.3 ° . Holes
were drilled through the APL to allow the probes to reciprocate into the plasma. When resting against
the outer hard stop, the tip of each probe head lies 3 mm below the CFC tiles. At the beginning of the
2011 experimental campaign, the system was tested under vacuum at several values of toroidal
magnetic field, with the tokamak at its nominal baking temperature of 120°C, but in the absence of
plasma. An example is shown in Figure 9 with B=2.73 T at the coil location. First, a voltage of V=-5 V
was applied for 100 ms to measure the electrical resistance of the drive circuit, R=2.07 Ω. A small
displacement of -1 mm was observed as the stirrup pressed the cushioning blade onto the outer hard
stop. Then, in order to verify that the position is correctly calculated, a voltage pulse of V=15 V was
applied for 100 ms to drive the probe to its inner hard stop. As soon as the positive voltage started
ramping up, the contact circuit opened. The coil current I was much less then the ohmic current V/R
that would be obtained without magnetic field, indicating appreciable back emf. After 60 ms, however,
the current jumped to the nominal ohmic value when the probe struck the inner hard stop, and the
contact circuit closed again. The calculated position corresponded well to the system geometry ( x max
=46 mm) with an accuracy of ±2 mm. After the pulse, the spring slowly dragged the probe back
towards the APL, but even after 350 ms it was still moving. A small negative voltage pulse was applied
at t=450 ms to force the probe onto the outer hard stop. It was encouraging to find that after integrating
the induced current for 600 ms, the reconstructed position signal returned exactly to zero. This
demonstrated that neither self induced currents nor numerical drift are significant sources of error.
A series of reciprocations with different insertion speeds was made in vacuum. The resulting
coil voltage found by the feedback routine is plotted in Figure 10, along with theoretical estimates for
different values of Neddy [cf Eq.(15)]. Within the scatter of the measurements and approximations made
in the model such as the neglect of sliding friction, it appears that eddy currents are negligible, as
predicted for this drive mechanism.
The signals measured during a feedback-controlled reciprocation into the plasma are shown in
Figure 11. The initial resistance calibration phase is not shown. During phase 3 the voltage is controlled
by the PI feedback algorithm in order to attain the target speed of 1 m/s. The voltage is then reversed in
phase 4 to bring the probe back towards the limiter. Since the absolute magnitude of applied voltage is
the same, the return speed is slightly higher than 1 m/s because the drive coil is no longer working
against the retaining spring. Finally the docking phase 5 gently halts the motion and places the probe
behind the CFC tiles. Throughout the reciprocation the acceleration was kept less than the operatorspecified value of amax=100 m/s2.
The feedback algorithm has proven to be reproducible. For example, when making multiple
reciprocations, the reconstructed position signals are identical to within 0.1 mm. In addition, it is safe
and reliable, allowing the probe operator to pay no heed to the specific value of magnetic field, nor the
position of the APL with respect to the LCFS. During the campaign, a total of 1075 reciprocations into
plasma were made. A scatter plot of the deepest position attained as a function of the total injected
power is shown in Figure 12. The APL is within the field of view of a tangential television camera, so
each reciprocation can be directly observed during a discharge. An image of simultaneous
reciprocations by the two probes is shown in Figure 13.
VII. Conclusion
A linearly reciprocating probe system with in-situ magnetic drive has been developed and tested
in the Tore Supra tokamak. Extensive analytical and numerical modelling were employed to dimension
the coil and develop a real-time feedback algorithm to control the probe motion. The coil was
dimensioned to operate in the overdamped regime for which magnetic braking dominates the force
exerted by the retaining spring. The only function of the spring is to keep the probe retracted when not
in use. Passive magnetic braking is used to bring the probe gently back to its resting position.
Nonetheless, we included a cushioning mechanism to reduce the shock if the probe is driven onto either
hard stop in case of failure of the control system. Care was taken to eliminate large loops from the
rotating coil support, in order to prevent eddy currents from circulating in moving parts. This reduces
the demands on the power supply. Thanks to the robustness of the real-time feedback algorithm and
safety checks, the probes can be programmed at the beginning of an experimental session and left to
make automatic measurements all day without human surveillance.
ACKNOWLEDGEMENTS
Numerous colleagues helped us with technical aspects of this project. We would especially like to
thank Hervé Cloez, Fréderic Faisse, Grégory Goubin, Patrice Leconte, Fabrice Leroux, Stéphane Rasio,
Jean-Marc Verger, and Bertrand Zago. This work, partially supported by the European Communities
under the contract of Association between EURATOM and CEA, was carried out within the framework
of the Priority Support Task "WP10-PWI-04-01-01/CEA/PS : Design and construction of dedicated
Langmuir probes for first wall measurements of heat and particle fluxes". The views and opinions
expressed herein do not necessarily reflect those of the European Commission. This work was mainly
supported within the framework of a grant awarded by "Direction de l’Economie Régionale, de
l’Innovation et de l’Enseignement Supérieur" of the Région Provence-Alpes-Côte d'Azur.
REFERENCES
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Figure 1: Probe drive assembly mounted on the
rear surface of the APL. Main components are
(1) the coil, (2) the stirrup, (3) the retaining
spring, (4) the probe shaft covered with a
diamond-like coating, and (5) the bronze guide
tube.
Figure 2: Schematic of pecker probe geometry.
The vertical direction on this picture corresponds
to the tokamak minor radius, along which the
probe moves a distance x. On the left, the probe
is drawn fully retracted (coil angle θ=θmin, probe
position x=0). On the right it is fully inserted
(coil angle θ=θmax, probe position x=46 mm). The
magnetic moment µ produced by the coil current,
and the lever arm l are indicated. θ=0
corresponds to the coil axis being perpendicular
to the magnetic field B, when the probe is half
way between its minimum and maximum
positions.
Figure 3: Model prediction of angular position of
coil after release from maximum position. Coils
with 56 and 266 windings are shown (full and
dashed curves, respectively). Solutions of Eq. (9)
are obtained without and with magnetic field
(thin and thick curves, respectively).
Figure 4: Time to retract the probe from
maximum to minimum position as a function of
the number of coil windings. Different values of
spring constant k and applied voltage V are
indicated. Dashed lines indicate N=56 and
N=266.
Figure 5: Operational domain of the coil
optimized for B=1.5 T (more restrictive than for
B=3 T). Shaded areas are forbidden
combinations of number of coil windings and
applied voltage. Optimal applied voltages are
shown for maximum and minimum magnetic
fields neglecting (thick curves) and including
eddy currents, Neddy=38, in the stirrup tread
(dashed curves).
Figure 6: Path of eddy current loop in the tread
of the stirrup induced by its rotation.
Figure 7: (a) Optimal applied voltage [Eq.(15)] for a range of coil winding numbers. (b) Drive
circuit current [Eq.(19)] during constant velocity entry phase of the probe. Full symbols
correspond to B=3T, open symbols to B=1.5 T. Squares, circles, and triangles correspond to
Neddy=0, 40, and 100, respectively.
Figure 8: Simulation results for N=160, Neddy=0,
and B=3 T. (a) Full curve (left hand axis) is the
probe position vs. time. The dashed curve (right
hand axis) is the error on the reconstructed
position signal due to neglecting the self
inductance of the coil. (b) Probe speed. (c) Probe
acceleration. (d) Thick curve = total coil current.
Dashed curve = induced current. Thin curve =
resistive component due to applied voltage. Thin
dashed-dotted curve = self current.
Figure 9: Test made for B=2.73 T. (a) Thick
curve = measured coil current. Thin curve =
applied voltage divided by drive circuit
resistance. (b) Current flowing through the
stirrup to tokamak ground. The vertical dashed
line indicates the instant when the probe struck
the inner hard stop. (c) Probe speed [cf Eq.(22)].
(d) Probe position relative to outer hard stop.
Figure 10: Coil voltage needed to drive the probe
at a given speed. The points are extracted from
the midpoint of the fast insertion phase. The
theoretical predictions [Eq.(15)] are indicated
for three values of eddy currents (characterized
by the equivalent winding number Neddy).
Figure 11: Reciprocation into discharge
TS47127. (a) Thick curve = measured coil
current. Thin curve = applied voltage divided by
drive circuit resistance. (b) Probe acceleration.
(c) Probe speed [cf Eq.(22)]. (d) Probe position
relative to outer hard stop. Phases of the
feedback routine are separated by dashed lines.
Figure 12: Scatter plot of deepest position of
each reciprocation relative to the LCFS as a
function of the total injected power (ohmic,
ICRH, plus LH).
Figure 13: TV image of simultaneous
reciprocations of the two pecker probes into the
SOL. The inset shows the lower probe manually
advanced to its deepest position during
installation.