Lecture 3: Cables and quenching

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					                      Lecture 3: Cables and quenching

                                                  Cables
                                                  • why cables?
                                                  • coupling in cables
                                                  • effect on field error in magnets


                                                  Quenching
Rutherford cable
                                                  • the quench process, internal and
used in all superconducting                         external voltages
accelerators to date
                                                  • decay times and temperature rise
                                                  • propagation of the normal zone
                                                  • quench protection schemes
                                                  • protection of LHC


Martin Wilson Lecture 3 slide1   Superconducting Magnets for Accelerators JUAS Feb 2006
                                       Why cables?
• for good tracking we connect synchrotron
  magnets in series
• if the stored energy is E, rise time t and
  operating current I , the charging voltage is
               1                    L I 2E
           E  LI 2           V       
               2                     t    It
  RHIC E = 40kJ/m, t = 75s, 30 strand cable
   cable I = 5kA, charge voltage per km = 213V
   wire I = 167A, charge voltage per km = 6400V

  FAIR at GSI E = 74kJ/m, t = 4s, 30 strand cable
   cable I = 6.8kA, charge voltage per km = 5.4kV
   wire I = 227A, charge voltage per km = 163kV

• so we need high currents!
                                                                     the RHIC tunnel
• a single 5mm filament of NbTi in 6T carries 50mA
• a composite wire of fine filaments typically has 5,000 to 10,000 filaments, so it carries 250A to 500A
• for 5 to 10kA, we need 20 to 40 wires in parallel - a cable

Martin Wilson Lecture 3 slide2          Superconducting Magnets for Accelerators JUAS Feb 2006
                                     Types of cable
• cables carry a large current and this generates a                  I
  self field                                                                               Bs
• in this cable the self field generates a flux between
  the inner and outer wires 
• wire are twisted to avoid flux linkage between the
  filaments, for the same reasons we should avoid
  flux linkage between wires in a cable
• but twisting this cable doesn't help because the inner
  wires are always inside and the outers outside

• thus it is necessary for the wires to be fully
  transposed, ie every wire must change
  places with every other wire along the
  length of the cable so that, averaged
  over the length, no flux is enclosed
• three types of fully transposed cable
  have been tried in accelerators
  - rope
  - braid
  - Rutherford

Martin Wilson Lecture 3 slide3            Superconducting Magnets for Accelerators JUAS Feb 2006
                                                                            Rutherford
                                                     •                        cable




• the cable is insulated by wrapping 2 or 3 layers of Kapton; gaps may be left to allow penetration
  of liquid helium; the outer layer is treated with an adhesive layer for bonding to adjacent turns.


• Note: the adhesive faces
  outwards, don't bond it
  to the cable (avoid
  energy release by bond
  failure, which could
  quench the magnet )




Martin Wilson Lecture 3 slide4        Superconducting Magnets for Accelerators JUAS Feb 2006
                                  Rutherford cable




    •     The main reason why Rutherford
          cable succeeded where others failed
          was that it could be compacted to a
          high density (88 - 94%) without
          damaging the wires. Furthermore it
          can be rolled to a good dimensional
          accuracy (~ 10mm).
    •     Note the 'keystone angle', which
          enables the cables to be stacked
          closely round a circular aperture




Martin Wilson Lecture 3 slide5          Superconducting Magnets for Accelerators JUAS Feb 2006
                            Coupling in Rutherford cables
•     Field transverse                                      
                                                            B             crossover resistance Rc
      coupling via crossover resistance Rc                                adjacent resistance Ra


                                                                                     Ra   Rc




•    Field transverse                                • Field parallel
     coupling via                                      coupling via
     adjacent                                          adjacent
     resistance Ra                                     resistance Ra
                                                                                                    
                                                                                                    B




                                     
                                     B

Martin Wilson Lecture 3 slide6           Superconducting Magnets for Accelerators JUAS Feb 2006
               Magnetization from coupling in cables
                                                                                 B`

 • Field transverse                            
                                            1 Bt c
                                    M tc           p N ( N  1)
   coupling via crossover                  120 Rc b                                           2b
   resistance Rc                                                                 2c
     where M = magnetization per unit volume of cable, p twist pitch, N = number of strands

 • Field transverse                                              
                                                               1 Bt c
   coupling via adjacent resistance Ra                  M ta      p
                                                               6 Ra b
      where q = slope angle of wires Cosq ~ 1


   • Field parallel                                              
                                                               1 Bp b                 (usually
     coupling via adjacent resistance Ra              M pa        p                  negligible)
                                                               8 Ra c

  • Field transverse                             M tc Ra N ( N  1)     R
                                                                    45 a
    ratio crossover/adjacent                     M ta Rc     20         Rc

   So without increasing loss too much can make Ra 50 times less than Rc - anisotropy

Martin Wilson Lecture 3 slide7           Superconducting Magnets for Accelerators JUAS Feb 2006
Controlling Ra and Rc                                                  1000                                             bare copper
                                                                                                                        untreated Staybrite
                                                                                                                        nickel

• surface coatings on the wires are used                                                                                oxidized Stabrite




                                                Resistance per crossover Rc m
                                                                                 100
  to adjust the contact resistance
• the values obtained are very sensitive
  to pressure and heat treatments used in
  coil manufacture (to cure the adhesive                                          10
  between turns)
• data from David Richter CERN
                                                                                   1




                                                                                 0.1
                                                                                       0   50          100        150        200        250
                                                                                                Heat treatment temperature C
Cored Cables

• using a resistive core
  allows us to increase Rc
  preferentially
• not affected by heat
  treatment

 Martin Wilson Lecture 3 slide8        Superconducting Magnets for Accelerators JUAS Feb 2006
                                 Long range coupling: BICCs
•     measuring the field of an accelerator
      magnet along the beam direction, we
      find a ripple
•     wavelength of this ripple exactly
      matches the twist pitch of the cable
•     thought to be caused by non uniform
      current sharing in the cable
•     Verweij has called them 'boundary
      induced coupling currents' BICCs
•     they are caused by non uniform flux
      linkages or resistances in the cable, eg
      at joints, coil ends, manufacturing
      errors etc.
•     wavelength is << betatron wavelength
      so no direct problem, but interesting
      secondary effects such as 'snap back'.                sextupole measured in SSC dipole at
                                                            injection and full field



Martin Wilson Lecture 3 slide9           Superconducting Magnets for Accelerators JUAS Feb 2006
                            Field errors caused by coupling
• plot of sextupole field                                     3
  error in an LHC dipole                                                                   0 A/sec         20 A/s
  with field ramped at                                        2                            35 A/s          50 A/s
  different rates




                                    sextupole field (Gauss)
• error at low field due to
                                                              1
  filament magnetization
• error at high field due to
                                                              0
   a) iron saturation
   b) coupling between
  strands of the cable                                        -1
• the curves turn 'inside
  out' because                                                -2
   - greatest filament
    magnetization is in
                                                              -3
    the low field region
    (high Jc)                                                      0      1     2      3       4       5       6    7     8         9
   - greatest coupling is in                                                                dipole field (T)
    the high field region
    (high dB/dt)                                                                                      data from Luca Bottura CERN

  Martin Wilson Lecture 3 slide10                                      Superconducting Magnets for Accelerators JUAS Feb 2006
                                  Cables: concluding remarks

  • accelerator magnets need high currents  cables
           - cables must be fully transposed
           - Rutherford cable used in all accelerators to date

  • can get coupling between strands in cables
          - causes additional magnetization  field error
          - control coupling by oxide layers on wires or resistive core foils




Martin Wilson Lecture 3 slide11          Superconducting Magnets for Accelerators JUAS Feb 2006
                                  Part 2: Quenching
                                                                              the most likely
                                                                              cause of death
 Plan                                                                         for a
                                                                              superconducting
 • the quench process                                                         magnet


 • decay times and temperature rise

 • propagation of the resistive zone

 • resistance growth and decay times

 • quench protection schemes

 • case study: LHC protection




Martin Wilson Lecture 3 slide12          Superconducting Magnets for Accelerators JUAS Feb 2006
                                     Magnetic stored energy
Magnetic energy density
           B2
        E                        at 5T E = 107 Joule.m-3         at 10T E = 4x107 Joule.m-3
           2m o


LHC dipole magnet (twin apertures)

E = ½ LI 2 L = 0.12H I = 11.5kA
E = 7.8 x 106 Joules

 the magnet weighs 26 tonnes
 so the magnetic stored energy is
 equivalent to the kinetic energy
 of:-

    26 tonnes travelling at 88km/hr



Martin Wilson Lecture 3 slide13                 Superconducting Magnets for Accelerators JUAS Feb 2006
       The quench process
                                                       • resistive region starts somewhere
                                                         in the winding at a point
                                                               - this is the problem!

                                                       • it grows by thermal conduction

                                                       • stored energy ½LI2 of the magnet
                                                         is dissipated as heat

                                                       • greatest integrated heat
                                                         dissipation is at point where the
                                                         quench starts

                                                       • internal voltages much greater
                                                         than terminal voltage ( = Vcs
                                                         current supply)

                                                       • maximum temperature may be
                                                         calculated from the current decay
                                                         time via the U(q) function
                                                         (adiabatic approximation)



Martin Wilson Lecture 3 slide14   Superconducting Magnets for Accelerators JUAS Feb 2006
                             The temperature rise function U(q)
    or the 'fuse blowing' calculation
    (adiabatic approximation)

     J 2 (T )  (q )dT   C (q )dq

        J(T) = overall current density,
        T = time,
        (q) = overall resistivity,
         = density, q = temperature,
        C(q) = specific heat,
        TQ= quench decay time.

                            qm    C (q )

o
        J 2 (T ) dT  
                            qo      (q )
                                           dq

                              U (q m )

         J o TQ  U (q m )
           2


     • GSI 001 dipole winding is
       50% copper, 22% NbTi,
       16% Kapton and 3% stainless steel                        • NB always use overall current density

        Martin Wilson Lecture 3 slide15         Superconducting Magnets for Accelerators JUAS Feb 2006
                    Measured current decay after a quench
                   8000                                                                 40


                                                                                        20
                   6000
                                                                                        0




                                                                                              coil voltage (V)
     current (A)




                   4000                                                                 -20
                                                                   current
                                                                   V lower coil         -40
                                                                   IR = L dI/dt
                   2000                                            V top coil
                                                                                        -60


                      0                                                                 -80
                          0.0     0.2              0.4            0.6             0.8
                                        time (s)

                                        Dipole GSI001 measured at Brookhaven National Laboratory

Martin Wilson Lecture 3 slide16          Superconducting Magnets for Accelerators JUAS Feb 2006
Calculating the temperature rise from the current
                   decay curve
                                    J 2 dt (measured)             U(q) (calculated)


                   6.E+16                                                                     6.E+16
 integral (J2dt)




                                                                                                       U(q) (A2sm-4)
                   4.E+16                                                                     4.E+16




                   2.E+16                                                                     2.E+16




                   0.E+00                                                                     0.E+00
                            0.0       0.2       0.4      0.60          200          400
                                     time (s)                           temp (K)


 Martin Wilson Lecture 3 slide17                  Superconducting Magnets for Accelerators JUAS Feb 2006
                                  Calculated temperature

                                                                          • calculate the U(q)
                                                                            function from known
                  400                                                       materials properties
                                                                          • measure the current
                                                                            decay profile
                  300
temperature (K)




                                                                          • calculate the maximum
                                                                            temperature rise at the
                                                                            point where quench
                  200                                                       starts
                                                                          • we now know if the
                                                                            temperature rise is
                  100                                                       acceptable
                                                                            - but only after it has
                                                                            happened!
                    0                                                     • need to calculate current
                        0.0       0.2              0.4              0.6     decay curve before
                                        time (s)                            quenching


Martin Wilson Lecture 3 slide18              Superconducting Magnets for Accelerators JUAS Feb 2006
                                  Growth of the resistive zone


                                                    the quench starts at a point and then grows
                                                         in three dimensions via the combined
                                                                    effects of Joule heating and
                                                                             thermal conduction




                                               *




Martin Wilson Lecture 3 slide19           Superconducting Magnets for Accelerators JUAS Feb 2006
                           Quench propagation velocity 1
• resistive zone starts at a point and spreads
  outwards                                                         resistive
• the force driving it forward is the heat generation                                      v
  in the resistive zone, together with heat                    temperature     qt
  conduction along the wire                                                              superconducting
• write the heat conduction equations with resistive
  power generation J2 per unit volume in left                     qo
  hand region and  = 0 in right hand region.                           distance    xt

                   q       q
                 k A   C A     hP(q  q 0 ) + J 2  A  0
              x    x       t

where: k = thermal conductivity, A = area occupied by a single turn,  = density, C = specific heat,
h = heat transfer coefficient, P = cooled perimeter,   resistivity, qo = base temperature
Note: all parameters are averaged over A the cross section occupied by one turn

 assume xt moves to the right at velocity v and take a new coordinate e = x-xt= x-vt

                                  d 2q v C dq h P              J 2
                                       +          (q  q 0 ) +      0
                                  de 2   k de k A                k

Martin Wilson Lecture 3 slide20               Superconducting Magnets for Accelerators JUAS Feb 2006
                            Quench propagation velocity 2
when h = 0, the solution for q which gives a continuous join between left and right sides at qt
gives the adiabatic propagation velocity
                                   1             1
                J  k          J  Loqt 
                                   2             2
                                                             recap Wiedemann Franz Law     (q).k(q) = Loq
     vad                                
                C qt  q 0   C qt  q 0 

what to say about qt ?
• in a single superconductor it is just qc
• but in a practical filamentary composite wire the current transfers progressively to the copper
                                       • current sharing temperature qs = qo + margin
                                       • zero current in copper below qs all current in copper above qs
                                       • take a mean transition temperature qs = (qs + qc ) / 2

                                        Jc                                 Cu
                                        Jop

                                                                          eff


                                                     qo qs           qc          qo   qs   qt     qc

 Martin Wilson Lecture 3 slide21              Superconducting Magnets for Accelerators JUAS Feb 2006
                            Quench propagation velocity 3
                                                                                                1
 the resistive zone also propagates sideways through               vtrans  ktrans 
                                                                                              2
 the inter-turn insulation (much more slowly)                                  
 calculation is similar and the velocity ratio  is:               vlong  klong 
                                                                                  

          Typical values           vad = 5 - 20 ms-1     0.01  0.03
                                                                   v            v
  so the resistive zone advances in
                                                                                                             v
  the form of an ellipsoid, with its
    long dimension along the wire



 Some corrections for a better approximation
• because C varies so strongly with temperature, it is better                          H (q c )  H (q g )
                                                                   Cav (q g ,q c ) 
  to calculate an averaged C from the enthalpy change                                     (q c  q g )
• heat diffuses slowly into the insulation, so its heat capacity should be excluded from the
  averaged heat capacity when calculating longitudinal velocity - but not transverse velocity
• if the winding is porous to liquid helium (usual in accelerator magnets) need to include a time
  dependent heat transfer term
• can approximate all the above, but for a really good answer must solve (numerically) the three
  dimensional heat diffusion equation or, even better, measure it!

 Martin Wilson Lecture 3 slide22           Superconducting Magnets for Accelerators JUAS Feb 2006
        Computation of resistance growth and current
                            decay
                                     start resistive zone 1                                        vdt
                                                                                                              vdt
                                                                                              *
   in time dt zone 1 grows v.dt longitudinally and .v.dt transversely

              temperature of zone grows by dq1  J2 (q1)dt /  C(q1)

                              resistivity of zone 1 is (q1)

       calculate resistance and hence current decay dI = R / L.dt
                                                                                                  vdt
                                                                                                            vdt
               in time dt add zone n:
       v.dt longitudinal and .v.dt transverse

temperature of each zone grows by dq1  J2(q1)dt /C(q1) dq2  J2(q2)dt /C(q2) dqn  J2(q1)dt /C(qn)

resistivity of each zone is (q1) (q2) (qn) resistance r1= (q1) * fg1 (geom factor) r2= (q2) * fg2 rn= (qn) * fgn


   calculate total resistance R =  r1+ r2 + rn.. and hence current decay dI = (I R /L)dt


                                     when I  0 stop
   Martin Wilson Lecture 3 slide23                   Superconducting Magnets for Accelerators JUAS Feb 2006
                         Quench starts in the pole region




                                                               *
                                             *



   the geometry factor fg depends on
   where the quench starts in relation
   to the coil boundaries




Martin Wilson Lecture 3 slide24          Superconducting Magnets for Accelerators JUAS Feb 2006
                           Quench starts in the mid plane




                                       *




Martin Wilson Lecture 3 slide25     Superconducting Magnets for Accelerators JUAS Feb 2006
                   Computer simulation of quench (dipole
                                GSI001)
                8000
                                                                   pole block
                                                               2nd block
                                                               mid block
                6000
  current (A)




                4000




                2000
                                  measured
                                  pole block
                                  2nd block
                                  mid block
                   0
                       0.0            0.1      0.2           0.3                0.4   0.5          0.6
                                                      time (s)



Martin Wilson Lecture 3 slide26                Superconducting Magnets for Accelerators JUAS Feb 2006
                              Computer simulation of quench
                                   temperature rise
                  600
                                      pole block
                                      2nd block
                  500                 mid block



                  400
temperature (K)




                  300



                  200


                                                                             from measured
                  100                                                        pole block
                                                                             2nd block
                                                                             mid block
                    0
                        0.0            0.2                       0.4                         0.6
                                                   time (s)

Martin Wilson Lecture 3 slide27         Superconducting Magnets for Accelerators JUAS Feb 2006
     Methods of quench protection:
                                                 1) external dump resistor

                                                      • detect the quench electronically
                                                      • open an external circuit breaker
                                                      • force the current to decay with a time
                                                        constant

                                                                       t
                                                                                              L
                                                        I  Ioe        t       where      t
                                                                                               Rp

                                                     • calculate qmax from

                                                                           τ
                                                                   2
                                                                  Jo          U (q m )
                                                                           2
      Note: circuit breaker must be able to
      open at full current against a voltage
      V = I.Rp               (expensive)



Martin Wilson Lecture 3 slide28         Superconducting Magnets for Accelerators JUAS Feb 2006
     Methods of quench protection:
                                                  2) quench back heater

                                                      •    detect the quench electronically

                                                      •    power a heater in good thermal contact
                                                           with the winding

                                                      •    this quenches other regions of the
                                                           magnet, effectively forcing the normal
                                                           zone to grow more rapidly
                                                            higher resistance
                                                            shorter decay time
                                                            lower temperature rise at the hot spot



      Note: usually pulse the heater by a capacitor, the             method most commonly used
      high voltages involved raise a conflict between:-               in accelerator magnets 
         - good themal contact
         - good electrical insulation


Martin Wilson Lecture 3 slide29        Superconducting Magnets for Accelerators JUAS Feb 2006
     Methods of quench protection:
                                               3) quench detection (a)
                          I
                                                                                       dI
                                                   internal voltage    V  IRQ   L          + Vcs
                                                   after quench                        dt
                                  V
                                                   • not much happens in the early stages -
                          t                          small dI / dt  small V
                                                   • but important to act soon if we are to
                                                     reduce TQ significantly
                                                   • so must detect small voltage
                                                   • superconducting magnets have large
                                                     inductance  large voltages during
                                                     charging
                                                   • detector must reject V = L dI / dt and pick
                                                     up V = IR
                                                   • detector must also withstand high voltage -
                                                     as must the insulation


Martin Wilson Lecture 3 slide30       Superconducting Magnets for Accelerators JUAS Feb 2006
      Methods of quench protection:
i) Mutual inductance
                                                         3) quench detection (b)
                                                              ii) Balanced potentiometer
                                                              • adjust for balance when not quenched
                                                              • unbalance of resistive zone seen as voltage
                                                                across detector D
                                            D
                                                              • if you worry about symmetrical quenches
                                                                connect a second detector at a different point




     detector subtracts voltages to give
                          di           di
              V L           + IRQ  M                                                        D
                          dt           dt

     • adjust detector to effectively make L = M
     • M can be a toroid linking the current
       supply bus, but must be linear - no iron!



 Martin Wilson Lecture 3 slide31                Superconducting Magnets for Accelerators JUAS Feb 2006
     Methods of quench protection:
                                           4) Subdivision
                                      • resistor chain across magnet - cold in cryostat
                 I                    • current from rest of magnet can by-pass the resistive
                                        section
                                      • effective inductance of the quenched section is
                                        reduced
                                              reduced decay time
                                              reduced temperature rise
                                      • current in rest of magnet increased by mutual
                                        inductance effects
                                              quench initiation in other regions
                                       • often use cold diodes to avoid
                                         shunting magnet when charging it
                                       • diodes only conduct (forwards)
                                         when voltage rises to quench levels
                                       • connect diodes 'back to back' so
                                         they can conduct (above threshold)
                                         in either direction


Martin Wilson Lecture 3 slide32   Superconducting Magnets for Accelerators JUAS Feb 2006
     Methods of quench protection:
                                  4b) Subdivision with quench back
     heater


                                                      • arrange for the subdividing
                                                        resistors to be in thermal contact
                                                        with the winding

                                                      • each resistor to contact a remote
                                                        section of winding – spread the
                                                        quench around




Martin Wilson Lecture 3 slide33        Superconducting Magnets for Accelerators JUAS Feb 2006
     Methods of quench protection:
                                           5) coupled secondary

                                              • arrange for the winding to be closely
                                                coupled to a short circuited secondary

                                              • typically the secondary will be the
                                                former on which the coil is wound.

                                              • the short circuited secondary reduces
                                                the effective inductance of the primary
                                                         - hence decay time is reduced

                                              • in addition, the secondary should be in
                                                thermal contact with the winding so that
                                                it quenches other regions




Martin Wilson Lecture 3 slide34   Superconducting Magnets for Accelerators JUAS Feb 2006
             LHC power supply circuit for one octant




circuit
breaker




       • diodes allow the octant current to by-pass the magnet which has quenched
       • circuit breaker reduces to octant current to zero with a time constant of 100 sec
       • initial voltage across breaker = 2000V
       • stored energy of the octant = 1.33GJ



Martin Wilson Lecture 3 slide35         Superconducting Magnets for Accelerators JUAS Feb 2006
                       Case study: LHC dipole protection
It's difficult! - the main challenges are:
1) Series connection of many magnets
• In each octant, 154 dipoles are connected in series. If one magnet quenches, the combined
  inductance of the others will try to maintain the current. Result is that the stored energy of all 154
  magnets will be fed into the magnet which has quenched  vaporization of that magnet!.
• Solution 1: put cold diodes across the terminals of each magnet. In normal operation, the diodes
  do not conduct - so that the magnets all track accurately. At quench, the diodes of the quenched
  magnet conduct so that the octant current by-passes that magnet.

• Solution 2: open a circuit breaker onto a dump resistor
  (several tonnes) so that the current in the octant is
  reduced to zero in ~ 100 secs.

2) High current density, high stored energy and long
  length
• As a result of these factors, the individual magnets are
  not self protecting. If they were to quench alone or
  with the by-pass diode, they would still burn out.
• Solution 3: Quench heaters on top and bottom halves
  of every magnet.

 Martin Wilson Lecture 3 slide36        Superconducting Magnets for Accelerators JUAS Feb 2006
       LHC quench-back heaters
 • stainless steel foil 15mm x 25 mm glued to outer
   surface of winding
 • insulated by Kapton
 • pulsed by capacitor 2 x 3.3 mF at 400 V = 500 J
 • quench delay - at rated current = 30msec
                     - at 60% of rated current = 50msec
 • copper plated 'stripes' to reduce resistance




Martin Wilson Lecture 3 slide37       Superconducting Magnets for Accelerators JUAS Feb 2006
             Diodes to by-pass the main ring current


            Installing the cold diode
           package on the end of an
                         LHC dipole




Martin Wilson Lecture 3 slide38         Superconducting Magnets for Accelerators JUAS Feb 2006
                  Quenching: concluding remarks
• magnets store large amounts of energy - during a quench this energy gets dumped in the winding
       intense heating (J ~ fuse blowing)             possible death of magnet
• temperature rise and internal voltage can be calculated from the current decay time
• computer modelling of the quench process gives an estimate of decay time
      – but must decide where the quench starts
• if temperature rise is too much, must use a protection scheme
• active quench protection schemes use quench heaters or an external circuit breaker
         - need a quench detection circuit which must reject L dI / dt and be 100% reliable
• passive quench protection schemes are less effective because V grows so slowly
        - but are 100% reliable
• protection of accelerator magnets is made more difficult by series connection
        - all the other magnets feed their energy into the one that quenches
• for accelerator magnets use by-pass diodes and quench heaters
• remember the quench when designing the magnet insulation


                                  always do the quench calculations before testing the magnet 

Martin Wilson Lecture 3 slide39       Superconducting Magnets for Accelerators JUAS Feb 2006

				
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