Stationary Magnetic Perturbations ('Locked Modes') and Edge Phenomena

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                                         ABSTRACT

         Stationary Magnetic Perturbations (‘Locked Modes’)
               and Edge Phenomena in TFTR Tokamak1
                    H. Takahashi, E. Fredrickson, K. McGuire, and A. Ramsey
                    Princeton Plasma Physics Laboratroy, Princeton University

Stationary Magnetic Perturbations (SMP’s), commonly known as ‘locked
modes,’ are investigated in TFTR. Ealier studies2 suggested the possibility
that the response of SMP sensors (‘locked mode detectors’) was in part pro-
duced by ‘halo currents’ that flow in the plasma scrape-off layer over part
of their path and in the tokamak structure over the rest of the path. In
the present study, the relationship is investigated between SMP’s and an
edge phenomenon called ‘blooms,’ which is thought to be caused by a con-
centrated power flow to a limiter surface. ‘Blooms’ are found to be almost
always accompanied by an SMP (magnetic phenomenon), suggesting that
they carry an electrical current, contrary to a traditional expectation. (Not
all SMP’s are accompanied by a ‘bloom,’ however.) These new observations
are consistent with the notion that SMP’s more generally are a consequence
of ‘halo currents.’
  Supported by DoE contract No. DE–AC02–76–CHO–3073
  1

  Several types of SMP’s were reported earlier — APS DPP, 1994(6R28), 1995(9P29), 1996(1S27); 7th Int.
  2


Toki Conf. on Plasma Physics and Nuclear Fusion, Toki City, Japan, Nov. 28 - Dec. 1, 1995, Paper T7-I4.
                                                                 APS-DPP97 TAK- 2


                             MOTIVATION

• Stationary Magnetic Perturbations (SMP’s), which are traditionally in-
  terpreted as locked modes, occur concurrently with adverse effects on
  tokamak discharges, such as loss of confinement and disruptions.
• If SMP’s are indeed locked modes caused by error fields, as a prevailing
  view claims, avoiding them in future tokamak reactors (such as ITER)
  would require a confining field that is uniform to 10−5 — a technically
  challenging and economically costly requirement.
• We study the SMP phenomenon in the hope that its thorough under-
  standing leads to a different, possibly far less costly, solution for avoiding
  adverse discharge effects associated with SMP’s.
                                                                                   APS-DPP97 TAK- 3

                                      HIGHLIGHTS

 • SMP’s and an edge phenomenon called ‘blooms’ are observed together
   with a high degree of concurrence.
 • ‘Blooms’ are traditionally thought to be an ‘edge atomic physics phe-
   nomenon.’ These new observations that ‘blooms’ are correlated with a
   magnetic signal suggest that ‘blooms’ carry electrical currents (i.e., akin
   to an electrical breakdown).
 • External and internal diagnostic data show that the SMP phenomenon
   more generally must involve a second source of magnetic signals in
   addition to MHD modes.
 • In the model proposed in earlier reports3 ‘halo currents’ serve as a sec-
   ond source of magnetic signals. (‘Blooms’ may involve such currents that
   cause ‘atomic physics processes’ on a limiter surface, perhaps because the
   currents become ‘anchored’ to particular locations on it.)
 • In our ‘halo current model,’ MHD modes, though usually observed
   prominently, are a secondary element in the SMP phenomenon.

 3
   SMP’s have been discussed in: APS DPP, 1994(6R28), 1995(9P29), 1996(1S27); 7th Int. Toki Conf. on
Plasma Physics and Nuclear Fusion, Toki City, Japan, Nov. 28 - Dec. 1, 1995, Paper T7-I4.
                                                                          APS-DPP97 TAK- 4

             LOCKED MODE PICTURE (CONVENTIONAL)

1. Slow down of the frequency of MHD modes4.
2. ‘Locking’ of MHD modes.
3. Growth of the amplitude of MHD modes while locked.

Oscillating perturbation currents of MHD modes generate oscillating eddy
currents in surrounding structures, which are retarded in phase due to finite
resistivity of structures, and exert secular (non-periodic) electromagnetic
forces on MHD modes, causing them (and plasma) to slow down.
External error fields, which exert only periodic forces to MHD modes while
the plasma is rotating, trap the modes in a ‘potential well’ once the plasma
momentum becomes too small to overcome the forces.
Error fields, which are prevented by the skin effect to enter the plasma
while it is rotating, can penetrate the plasma as it slows down and stops
rotating. Destabilizing resonant components of error fields reach relevant
rational surfaces, and cause MHD modes to be excited, or render MHD
modes more strongly unstable, if they already exist.
 4   So-called purely growing locked modes lack oscillating precursors.
                                                                                           APS-DPP97 TAK- 5

                    ‘LOCKED MODE’ PICTURE5 FOR TFTR

1. Slowing and stationary (or ‘locked’) perturbations, both internal and
   external, do exist (no quarrels here).
2. Low-order tearing-type MHD modes are responsible for only a fraction
   of measured signals of ‘locked mode’ detectors.
3. Slow down of the frequency, or cessation of rotation, has little effects on
   the amplitude of MHD modes.
4. Error fields are not directly involved in ‘locked modes.’
5. Detailed plasma properties, probalbly in the scrape-off, but not directly
   bulk plasma properties, determine generation of locked modes.
6. A second phenomenon exists that has powerful influences on transport,
   and also generates a bulk of ‘locked mode’ detector response. We think
   the phenomenon is ‘halo currents.’

Since MHD modes are argued here to be only a secondary element of locked
modes, a more general term, Stationary Magnetic Perturbations (SMP’s),
is used in our model.
 5   The model was constructed from observations described in this report as well as earlier ones.
                                                                                                       APS-DPP97 TAK- 6


                          DISCHARGE WITH SMP AND ‘BLOOM’

                #87031                                          (a)                  Fig. 1 An overview of dis-
            2                                                             40
                                                                                     charges with SMP and ‘bloom’




                                                                              (MW)
  (MA)




                    Ip
            1                                                             20         events (see below for details).
    Ip




                                                                                Pb
                                           Pb
                                                                                     (a) Two discharges had identi-
            0                                                             0
                                                                (b)
                                                                                     cal Ip and Pb waveforms. (b)
            6                                  A
                                                                                     In Discharge A, an edge event,
n (m^-3)




            4
                                                                                     termed ‘bloom’ in TFTR lingo,
19




            2 A: #87031
              B: #87030
                                      B
                                                           FM-NEBAR
                                                                                     took place around 4.2 sec when
            0                                                                        density rose strongly. (An ear-
            2                                                   (c)
                                                                                     lier density peak was caused by
 B r (G)




                                                       3
            0                                                                        unrelated Li-pellet injection.)
   DN




                                           2
            -2 #87031 -
                                 1
                                                                                     In Discharge B, no bloom oc-
               #87030                                      ML-BR-DN
            -4                                                                       curred. (c) and (d) An SMP
            2                                                   (d)                  event at ‘1’ and ‘2’ occurred
  B r (G)




            0
                                                       3
                                                                                     concurrently with bloom.
   FP




            -2 #87031 -                    2
                                 1
                 #87030                                    ML-BR-FP
            -4
               0          2       4                6                  8
                              time (sec)
                                                                                                         APS-DPP97 TAK- 7


                                                           ‘COMPOUND’ SMP


                         10                                                                  Fig. 2 Mirnov coil
                                                                                 (a)         and SMP sensor sig-
dB/dt (T/sec)




                                                                                             nals in an SMP event.
                           0                                                                 (a) Oscillation fre-
                                                                                             quency of Mirnov signal
                                                                            #87031           slows down. (b) SMP
                                     DMM-IN-08-S
                         -10                                                                 signal builds up secu-
                                                                                             larly while oscillating at
                                                                                 (b)         the same time. We call
                           0                                                                 this type a ‘compound’
            (G)




                                                                                             SMP for this reason.
                DN




                          -2
                     r




                                                                            #87031 -
            B




                                                                            #87030
                                     ML-BR-DN
                          -4
                               4.0                 4.2                4.4              4.6
                                                         time (sec)
                                                            APS-DPP97 TAK- 8
                       ‘BLOOMS’ IN TFTR

• In some TFTR discharges an unusual edge phenomenon occurs that
  causes a rapid increase in light emission from hydrogenic atoms and
  carbon impurity ions. A concomitant increase in plasma density first ap-
  pears at the plasma edge and then propagates inward. Radiated power
  and visible Bremsstrahlung also increase. Energy confinement degrades
  significantly.
• The ‘bloom’ has traditionally been considered to involve only particles
  and energy, but not electrical currents.
• But concurrent observations of ‘blooms’ almost always with an SMP,
  which is a magnetic phenomenon, suggest that ‘blooms’ carry electrical
  currents. ‘Blooms’ may be a phenomenon akin to an electrical breakdown
  in scrape-off plasmas.
                                                                         APS-DPP97 TAK- 9


                              ‘BLOOMS’ IN TFTR
         6                                6
                 Pellet                        Carbon Light (a.u.)
                                 Bloom

         3                                3

             Edge Line Density
             (10^15/m^2)
         0                                0
             H-alpha Light (a.u.)
       1.0

                                         0.1

       0.5

                                               Energy Conf. Time (sec)
       0.0                               0.0
             3            4          5         3          4          5
                    time (sec)                       time (sec)


Fig. 3 In a ‘bloom’ light emission increases from hydrogenic atoms and
carbon impurity ions. Density increases first at edge. Energy confinement
degrades. (The peak at 3.2 sec is an unrelated Li-pellet injection.)
                                                                             APS-DPP97 TAK- 10


           CONCURRENCE OF SMP’S AND BLOOMS


                                                         1.0
 30


 25
                                                  -50               50        100       150
                        SMP No                          -1.0
 20




                                  Br Change (G)
                        SMP
 15                                                     -2.0
                        Maybe

 10                     SMP Yes                         -3.0


  5
                                                        -4.0
                                                               Edge Density Change (a.u.)
  0
          Blooms




Fig. 4 Nearly all ‘bloom’ shots had                 Fig. 5 Increase in edge density dur-
a concurrent SMP (but not all SMP’s                 ing a ‘bloom’ event is correlated with
have a ‘bloom’).                                    increase in SMP signals.
                                                                             APS-DPP97 TAK- 11


                EVIDENCE FOR SOURCE OF MAGNETIC SIGNALS

                2                                                   Fig. 6 Both difference
                        (a)                                         and sum of SMP signals
                                                                    from a toroidally oppo-
B DN- (G)




                0
                                                                    site sensor pair are ex-
                                                                    amined. The sum and
            r




                -2                                     #87031 -
                         DML-BR-D -                                 difference signals con-
                         DML-BR-N                      #87030
                                                                    tain a secularly growing
                -4
                                                                    component. The dif-
                                                                    ference signal contains
                0                                      #87031 -     also a slow oscillating
                        (b)
                                                                    component. The sec-
BDN+ (G)




                                                       #87030
                                                                    ular component cannot
                -1                                                  be produced by MHD
            r




                         DML-BR-D +
                         DML-BR-N                                   modes alone. The SMP
                                                                    signal must have contri-
                -2
                  4.0             4.2      4.4       4.6        4.8 butions from an addi-
                                                                    tional source.
                                        time (sec)
                                                              APS-DPP97 TAK- 12



         MODEL OF SMP AND ‘HALO CURRENTS’

• We postulate ‘halo currents’ flowing through scrape-off plasmas and toka-
  mak structures. They may sometimes be rotating at small amplitudes,
  but may get ‘anchored’ at some preferred limiter points at large ampli-
  tudes.
• ‘Halo currents’ fit the bill in explaining many aspects of the SMP phe-
  nomenon, but not ‘MHD perturbation currents.’
• ‘Halo currents,’ interrupted by limiters, are incomplete helices and uni-
  directional while ‘MHD perturbation currents’ (placed at x- and o-points)
  are complete helices and bi-directional. These different geometrial char-
  acteirstics result in important differences in effects the currents produce.
• First, ‘halo currents’ can produce secular and oscillating components in
  both difference and sum signals, but not ‘MHD perturbation currents.’
  Second, ‘halo currents’ produce a much greater radial field than ‘MHD
  perturbation currents’ (see below). Third, ‘halo currents’ act like dynam-
  ically introduced error fields, and serve as a mechanism to slow down and
  lock MHD modes.
                                                               APS-DPP97 TAK- 13


               ‘INTERRUPTED’ HALO CURRENTS




Fig. 7 Halo currents that are inter-    Fig. 8 ‘Interrupted’ halo currents pro-
rupted by structures are discrete and   duce much greater Br (top ‘curve’)
incompletely helical ‘bundles.’         than completed helical currents (bot-
                                        tom) for a unit current (1 kA).

 We think that several kA of ‘interrupted halo currents’ flow in a tokamak
 with a few MA of plasma current. Currents of such a size are compatible
 with observed SMP detector signals.
                                                               APS-DPP97 TAK- 14



EVIDENCE FOR SOURCE OF MAGNETIC SIGNALS — Cont.

• We observe that waveforms (i.e., time variation) of Mirnov signals resem-
  bled a regular sinusoid well before the ‘mode locking’ time, but became
  distorted at later times. This can be evidence for the presence of a source
  of magnetic signals in addition to, or in place of, MHD modes.
• We note, however, that waveforms can be distorted either because a
  spatially regular perturbation structure rotates at irregular speeds, or
  because a spatially irregular structure rotates at a regular (or irregular)
  speed.
• A Lissajous diagram of a pair of Mirnov signals can be used to eliminate
  the time as a variable, and hence to discern the spatial coherence of a
  perturbation structure to distinguish between these possibilities.
• We will conclude that the waveform distortion of external magnetic sig-
  nals was a result of spatial distortion due to an additional source of mag-
  netic signals, for example, ‘halo currents.’ Comaprisons with Lissajous
  diagrams of internal perturbations will reinforce this conclusion.
                                                                                       APS-DPP97 TAK- 15


                    MIRNOV SIGNALS ‘WELL BEFORE’ LOCKING

           20
                #87031                                   (a)
                θ = 112.5 deg
 (G)




           10
       θ
 B




                                            DMM-IN-06-S (INT)
            0
           20
                                                         (b)
 (G)




           10
       θ
 B




                #87031
                θ = 153.7 deg               DMM-IN-08-S (INT)
            0
           20
                #87031                                   (c)
                θ = 225.0 deg
 (G)




           10
       θ
 B




                                            DMM-IN-10-S (INT)
            0
             4000                  4005                    4010
                                time (ms)


Fig. 9 Waveforms of Mirnov signals                                Fig. 10 Lissajous diagrams of a pair
show time coherenece at all poloidal                              of Mirnov signals (δB1 vs. δB2) show
locations.                                                        space coherence over many cycles.
                                                                                          APS-DPP97 TAK- 16

                      MIRNOV SIGNALS ‘JUST BEFORE’ LOCKING

           40
                   #87031                                   (a)
                   θ = 112.5 deg
 (G)




           20
       θ
 B




                                               DMM-IN-06-S (INT)
            0
           40
                   #87031                                   (b)
                   θ = 153.7 deg
 (G)




           20
       θ
 B




                                               DMM-IN-08-S (INT)
            0
           40
                                                            (c)
 (G)




           20
       θ
 B




                   #87031
                   θ = 225.0 deg               DMM-IN-10-S (INT)
            0
            4180                     4200                     4220
                                   time (ms)


Fig. 11 Waveforms of Mirnov signals                                  Fig. 12 Lissajous diagrams of a pair
show distorted time coherenece at all                                of Mirnov signals (δB1 vs. δB2) show
poloidal locations.                                                  distorted space coherence.
                                                                                             APS-DPP97 TAK- 17

                         MIRNOV SIGNALS ‘AROUND’ LOCKING

           80
                #87031                                          (a)
                θ = 112.5 deg
 (G)




           40
       θ
 B




                                            DMM-IN-06-S (INT)
            0
           80
                #87031                                          (b)
                θ = 153.7 deg
 (G)




           40
       θ
 B




                                            DMM-IN-08-S (INT)
            0
           80
                #87031                                          (c)
                θ = 225.0 deg
 (G)




           40
       θ
 B




                                            DMM-IN-10-S (INT)
            0
            4200                   4300                          4400
                                time (ms)


Fig. 13 Waveforms of Mirnov sig-                                        Fig. 14 Lissajous diagrams of a pair
nals show strongly distorted time co-                                   of Mirnov signals (δB1 vs. δB2) show
herenece at all poloidal locations.                                     strongly distorted space coherence.
                                                                                                          APS-DPP97 TAK- 18


                             INTERNAL PERTURBATIONS — ISLANDS


                 (a)                                                                 (b)
                                              O : 4201.0 ms                                                    O : 4200.0 ms
             6                                X : 4203.0 ms                      6                             X : 4202.0 ms




                                               X
                                                                                 4                               X
             4




                                                                    Te (keV)
Te (keV)




                                 O
                                                                                                   O
             2                                                                   2                  Island
                                     Island             F                                                               F


                 #87031                                                              #87031              m
                 GPC-1                                                               GPC-2
             0                                                                   0
                       2.5              3.0                   3.5                          2.5           3.0                   3.5
                                R (m)                                                            R (m)


           Fig. 15 Te profiles from GPC-1 signals                               Fig. 16 Te profiles from GPC-2 signals
           show an island structure ‘just before                               show an island structure ‘just before
           locking time.’                                                      locking time.’
                                                                 APS-DPP97 TAK- 19

    SPACE COHERENCE OF INTERNAL PERTURBATIONS




Fig. 17 Lissajous diagrams of a pair      Fig. 18 Lissajous diagrams of a pair
of Te perturbation signals (δTe1 vs.      of Te perturbation signals (δTe1 vs.
δTe2) ‘well before locking time’ — good   δTe2) ‘just before locking time’ — still
space coherence.                          good space coherence unlike external
                                          magnetic signals.
                           APS-DPP97 TAK- 20


ISLAND GROWTH


                Fig. 19 Island width and
                rotation frequency mea-
                sured by ECE. Island
                is growing before ‘mode
                locking,’ with a growth
                rate that is little affected
                by mode slow down. Is-
                land does not grow after
                locking (points after lock-
                ing in gray), contrary to a
                theoretical expectation.
                                                               APS-DPP97 TAK- 21


                              SUMMARY

1. A source of magnetic signals in addition to, or in place of, MHD modes
   is involved in the SMP phenomenon.
2. ‘Halo currents’ in a scrape-off plasma are a possible additional source of
   magnetic signals in the SMP phenomenon.
3. A ‘bloom’ is nearly always accompanied by an SMP (but the converse is
   not true), and hence involves electrical currents; A ‘bloom’ is akin to an
   electrical breakdown in a scrape-off plasma.