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Unit Protection of Superconducting accelerator magnets

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					                      Unit 18
     Protection of Superconducting accelerator
                      magnets

                         Soren Prestemon and Paolo Ferracin
                           Lawrence Berkeley National Laboratory (LBNL)
                                                       Ezio Todesco
                      European Organization for Nuclear Research (CERN)

USPAS June 2007, Superconducting accelerator magnets
                                              Scope of the Lesson


                      Magnet protection
                            Overview
                            Critical time constants
                            Quench propagation
                            Methods of passive and active protection
                            Design issues
                            Examples
  Following closely the presentation of Wilson “Superconducting magnets”




USPAS June 2007, Superconducting accelerator magnets                   Magnet Protection 16.2
                                                       References

                      Follows closely the presentation of Wilson
                            “Superconducting magnets”

      Also thanks to:
             Arnaud Devred, “Argonne Lectures”
             Mess, Schmueser, Wolff, “Superconducting Accelerator Magnets”
             Al McInturff, private communications
             Michael A. Green, private communications
             P. Bauer, S. Feher, M. Lamm “Quench Protection Model and the
             LHC IR-Quadrupole Case”
             Nist Monograph 177, “Properties of Cu and Cu alloys at Cryogenic
             Temperatures”



USPAS June 2007, Superconducting accelerator magnets                Magnet Protection 16.3
                                                       Overview




USPAS June 2007, Superconducting accelerator magnets              Magnet Protection 16.4
                                           Critical time constants

      In the case of a quench, the energy stored in the magnetic field will be
      converted to heat
             Magnet protection involves appropriately distributing the stored energy so
             as to avoid damaging the magnet
                   The “hot spot” temperature is the peak temperature attained on the conductor
                   during a quench
                   Damage can range from epoxy damage or reduced dielectric strength to melting
                   of stabilizer!
                   More likely, excessive temperature gradients can damage the magnet due to
                   differential expansion of materials
                           thermal expansion varies little for most materials below ~100K => safe goal


             Under extreme conditions it may be necessary to bring some of the energy
             out to room-temperature resistive dumps




USPAS June 2007, Superconducting accelerator magnets                                             Magnet Protection 16.5
                                              The simplest model

      The characteristic time for the magnet energy to be converted to
      thermal energy is τm, defined by:
                                τm
                                                    1 2
                                 ∫ I (t ) R(t )dt = 2 LI 0
                                        2

                                 0


                                     Joule heating     Magnetic stored energy

      Magnet protection concerns system design to safely convert the
      magnetic energy into thermal energy without risk of damaging
      components
             Minimize peak voltages
             Minimize peak temperatures and temperature gradients

               GOAL: ELIMINATE RISK OF DAMAGE TO THE MAGNET

USPAS June 2007, Superconducting accelerator magnets                            Magnet Protection 16.6
                                                       Definition of MIITs

      Consider the most basic energy conservation statement for a conductor:
             Energy is deposited via Joule heating
             The heat results in an increase in temperature based on the specific heat
                   assume that the full conductor + insulation contributes to the heat capacity
                   assume that only the stabilizer (e.g. Cu) contributes to the Joule heating
                   Neglect any longitudinal heat transfer

                                                       ρcu (T )
                                          I (t )   2
                                                                    dt = Atot ∑ γ i c p ,i (T )dT
                                                         Acu                           i



      The resulting energy balance defines the most basic of parameters for
      quench protection in a magnet, “MIITS”:

                              ∞
                                                            Tmax    ∑γ c   i p ,i   (T )
                          ∫                                    ∫
                                      2
                                  I (t ) dt = Acu Atot               i
                                                                                           dT = 106 MIITs(Tmax )
                            0
                                                               T0
                                                                         ρcu (T )



USPAS June 2007, Superconducting accelerator magnets                                                               Magnet Protection 16.7
                              Example of quench propagation




USPAS June 2007, Superconducting accelerator magnets          Magnet Protection 16.8
                                                  Typical Scenario

        Consider the basic protection scenario:
        1.    The magnet is superconducting and at some state I=I0
        2.    A quench occurs at some location in the magnet
        3.    As the normal zone propagates, a resistive voltage is generated
        4.    The detection system determines the existence of a quench once sufficient
              voltage has developed; a time ∆tdet has elapsed
                                                                                   L
        5.    The current in the magnet begins to decay with a time constant τ R =
                                                                                   R
                                                       I

       The resistance R is the sum                     I0
       of internal normal zone
       resistance and any external
       dump resistor connected to
       the system; L is the total
       system inductance,
                                  1 2                                            t
                           E=       LI
                                  2                         τdet     τR
USPAS June 2007, Superconducting accelerator magnets                        Magnet Protection 16.9
                                  Quench propagation velocity

      We have seen previously that a thermal instability can lead
      to the development of a quench
      A quench is characterized in its early state by
             a normal zone propagating away from the initiation point
             A fast temperature rise in the normal region as Joule heat is
             deposited
      The equation developed for initial stability analysis holds
      for quench propagation as well
             Need to couple in the electric circuit equation(s) to determine the
             current decay rate
             Although the initial quench propagation is longitudinal, transverse
             thermal conduction will initiate quenches in neighboring conductors
             as well


USPAS June 2007, Superconducting accelerator magnets                   Magnet Protection 16.10
                                  Quench propagation velocity

      The initiation of a quench is subject to a transient (typically high) initial
      velocity that quickly stabilizes to a ~constant propagation velocity vprop
      For “adiabatic” coils, i.e. where thermal transfer is only via conduction
      (examples: potted coils, cryogen-free magnets), the quench propagation
      velocity vprop=vad can be estimated as:

                                              1/ 2
                   J  ρ cu kav 
            vad ≈
                  Cav  ∆θ 
                                                     BSCCO
                                                       simulation
                   1
            Cav =     ∑ Aiγ iC p,i
                  Atot i                                                            vad

         Assumptions:
         •1D propagation
         •Constant propagation velocity
         •Properties independent of temperature
         •Do not include epoxy in averages (k too low to benefit)
USPAS June 2007, Superconducting accelerator magnets                   Magnet Protection 16.11
                  Current margin, propagation velocity and
                                protection
      Note: the quench propagation velocity is a function of the
      temperature margin
          Temperature margin is a function of the fraction Iop/Ic
        => Most dangerous point from a protection perspective is often
          somewhat less than peak current!




USPAS June 2007, Superconducting accelerator magnets              Magnet Protection 16.12
                                         Transverse propagation

      The thermal conductivity through turn insulation is very poor (~10-100
      times slower)
      Including transverse propagation does not change the longitudinal
      propagation velocity estimate (time scales are very different)
      Transverse propagation can be modeled using the same formula as for
      longitudinal propagation:
             Replace kl => kt
             Since time scale is slower, include Cp of insulation


                                                                  1/ 2
                                                            κ tr       C p ,metal
                                        vtr ,ad ≈ vl ,ad    
                                                            κl          C p ,all


USPAS June 2007, Superconducting accelerator magnets                                  Magnet Protection 16.13
                                      Voltages during a quench

      We have seen that the normal zone growth results in a rising
      resistance; where is the voltage coming from?
             Uncontrolled, the power supply will try to maintain current until its
             voltage limit is reached
             Typically a voltage threshold on the power supplies is used to diagnose a
             quench, and the power supplies are shut off
             Once current begins to decay, voltage does not come from the power
             supply – it is generated by the magnet inductance!
                            dI (t )
                          L         = I (t ) Rn (t )
                               dt
                                    dI (t )
                          Vn (t ) =         [ L − M (t )]
                                     dt

             The mutual inductance between the normal zone and the coil is key in
             predicting the peak voltage appearing within the magnet

USPAS June 2007, Superconducting accelerator magnets                       Magnet Protection 16.14
                             Self (passive) or active protection

      We have seen that the normal zone propagates at a velocity
                                                                        1/ 2
                                                   J          ρ cu kav 
                                            vad ≈             ∆θ 
                                                  Cav                  
      Using the previous scenario, we can estimate the resistance required for
      self-protection (i.e. no active enhancement of the normal zone or
      extraction of energy):
                                 ∆τ det                ∞      R
                                                             − t
                                   ∫      I 02 dt + ∫ I e  2
                                                           0
                                                              L
                                                                   dt = 106 MIITs
                                   0                   0
      Under rare circumstances the magnets normal zone propagates
      sufficiently fast to provide ample resistance
             Caution: the normal zone propagation depends on the temperature margin,
             so the most dangerous operating point from a protection perspective may
             be well below the peak operating current

USPAS June 2007, Superconducting accelerator magnets                                Magnet Protection 16.15
                                        Calculation of resistance

      Neglecting variations of resistance vs time, we get an effective resistance
      to design to:

                                                         I 02 L
                                        R=                        ∆τ det

                                                106 MIITs −         ∫
                                                                    0
                                                                           I 02 dt


      Note that the normal zone resistance is a function of time, temperature
      and field (via magnetoresistance)



                                                       vad t          dx
                                R(t , T , B ) = ∫ ρ (T ( x), B ( x) )
                                                 − vad t              Acu

USPAS June 2007, Superconducting accelerator magnets                                 Magnet Protection 16.16
                                  Importance of stabilizer RRR

    The current decay time constant is
    decreased by increasing the
    stabilizer resistance
           Note the difference between protection
           and stability requirements:
                 Protection: lower RRR advantageous
                 (shorter decay time)
                 Stability: higher RRR advantageous
                 (enhanced dynamic stability)
           At higher fields, magnetoresistance is
           significant:
                 Magnetoresistance at high operating
                 fields tends to “water down” the impact
                 of any choice of RRR
                         low RRR materials are mildly impacted
                         by magnetoresistance
                         High RRR materials are heavily
                         impacted

USPAS June 2007, Superconducting accelerator magnets             Magnet Protection 16.17
                                             Importance of fast
                                           normal zone growth: I
      From the basic MIITs analysis, fast normal zone growth is
      needed to avoid unreasonable hot-spot temperatures




USPAS June 2007, Superconducting accelerator magnets               Magnet Protection 16.18
                                            Importance of fast
                                          normal zone growth: II
      From the simple circuit analysis, fast normal zone growth is
      needed to enhance the mutual inductance M between the
      normal zone and the magnet, essential to limit peak
      voltages within the windings




USPAS June 2007, Superconducting accelerator magnets               Magnet Protection 16.19
                                              Protection methods

      For many (most) aggressively designed accelerator magnets the normal
      zone growth by itself is insufficient to provide the requisite resistance.
      How can we enhance the resistance?
      Method I:
             Add an external dump resistor
      Method II:
             Introduction of coupled secondary circuit(s)
                   Can take the form of a shorted secondary or coil subdivision
                   Mutual inductance between coil and secondary circuit results in voltage and
                   hence dissipation of energy in secondary.
                   May yield quenchback
      Method III:
             Force more of the magnet to go normal by applying heat
                   Heaters can be tailored to the magnet
                   Heater circuitry designed to provide fast thermal rise with reasonable voltages
                   Thermal diffusion time for heat to progress from heater to coil critical

USPAS June 2007, Superconducting accelerator magnets                                 Magnet Protection 16.20
                                     A simple Active protection

    The simplest enhancement to protection is the addition of
    an external resistor Rext
           If Rext>Rn, it will dominate the current decay rate
           The method is active because it requires switching
           Danger: the external resistor will see a voltage V=IopRext
                 If V is too large:
                         it will be difficult to switch
                         The leads and other components could be compromised                  Cold
           Key requirement is fast quench detection
           Additional advantage: heat dissipated in Rext does not impact
           cryogenics

           Unfortunately, most accelerator magnets operate at high Jc and high
           current, so realistic voltages impose small Rext

USPAS June 2007, Superconducting accelerator magnets                           Magnet Protection 16.21
                Passive protection via a coupled secondary
                                  circuit
       A shorted secondary circuit inductively coupled to the magnet will see
       a voltage Vs(t)~MdI(t)/dt, where M is the mutual inductance between
       the circuits (subscript m refers to magnet, s to secondary):      Wilson
    dI m (t )                          dI (t )
  Lm          + Rn (t ) I m (t ) + M s = 0                                     Im
       dt                                 dt
                                                                                    Lm
    dI (t )                          dI (t )
  Ls s + Rs (t ) I s (t ) + M m = 0
      dt                                dt
                                                                                    Rn
              M 2  dI m (t )                                   MRs (t )
  ⇒ Lm 1 −                       + I m (t ) Rn (t ) − I s (t )          =0
         Lm Ls  dt                                              Ls

       In most scenarios the winding mandrel is designed as the secondary.
       Note that the secondary generates heat during ramping as well;
       secondary circuits are typically used in magnets designed for long-
       term steady-state fields
             Typical application: DETECTORS
USPAS June 2007, Superconducting accelerator magnets                                     Magnet Protection 16.22
                                                Secondary circuits

        A sizeable fraction of the magnet energy can be transferred to the
        secondary, thereby decreasing:
        1.    the peak voltage within the magnet
        2.    the peak hot-spot temperature
        Just how helpful is the secondary?

                           M 2  dI m (t )                               MRs (t )
                    Lm 1 −                + I m (t ) Rn (t ) − I s (t )          =0
                        Lm Ls  dt                                        Ls

        If the secondary circuit current is small, the circuit equation is
        essentially that of the magnet with a reduced inductance and hence a
        reduced time constant:
                                   '          M2           Note: if Is ~Im within τm’,
                                  Lm = Lm 1 −              the analysis does not
                                              Lm Ls        hold and the system
                                                           L'm                   needs numerical
                                                       ⇒τ = τm
                                                         '
                                                         m                       treatment
                                                           Lm
USPAS June 2007, Superconducting accelerator magnets                                       Magnet Protection 16.23
                                    The concept of quench-back

        The coupled secondary is subjected to a thermal load based
        on the induced currents and its resistance
              If the secondary is in close thermal contact with the main coil, the
              heat in the secondary can serve to further quench the main coil

                              => QUENCH-BACK


        The term quench-back also applies to other mechanisms of inducing
        “global” or distributed quenching from dIm/dt
              Example: AC losses can induce quenching if sufficiently intense




USPAS June 2007, Superconducting accelerator magnets                       Magnet Protection 16.24
                                Requirements for Quenchback

  What are the basic requirements for
  quench-back to occur?                                            Im
    1.   The secondary must heat above the current                                 Im
         sharing temperature of the coil (+margin for
         thermal diffusion)                                        Is
                                                                                            Is
    2.   The secondary must be in good thermal
         contact with the magnet
                                                                                                 t
    3.   The thermal rise time τdif for the secondary
                                                                    τR
         must be significantly shorter than the                                Tsecondary
         magnets characteristic time constant         Tc
                this is the time constant associated with    Tcs
               combined normal zone growth, external
                                                             Top
               resistor, and the inductive contribution from                       Tcoil
               the secondary
                                                                                                 t
                                                                        τdif
USPAS June 2007, Superconducting accelerator magnets                           Magnet Protection 16.25
                           Example using coupled secondary:
                                        CMS
      The CMS Detector solenoid at the LHC is a massive detector:
             Peak field of ~4T
             6m diameter
             12.5m length
      Solenoid
             4-layer Rutherford-like cable
             External aluminum cylinder
             Cooled using a thermosiphon
             2.6GJ stored energy, 12kJ/kg


P. Fazilleau et al., “Analysis and Design of
the CMS Magnet Quench Protection”,
IEEE Trans. App. Sup. Vol 16, no2, June
2006



USPAS June 2007, Superconducting accelerator magnets            Magnet Protection 16.26
                        CMS calculated quench performance

      Quench system characteristics:
             The longitudinal quench velocity is slow: ~1.3m/s
             The quench performance comes from the coupling to the cylinder which
             develops up to ~480kA
             The cylinder causes the remainder of the coil to quench after ~30s




USPAS June 2007, Superconducting accelerator magnets                    Magnet Protection 16.27
                       Passive protection by coil subdivision

      Subdividing the coil into sections, each
      with a resistance in closed circuit, can
      reduce the decay time constant
             A normal zone in one section will result in the
             current from a different section being shunted
             through a resistance
             By putting the resistances in close thermal
             contact with the magnet sections, the shunted
             current can serve as a passive heater to rapidly
             enlarge the quench zone
                   Similar to quench-back
             The technique is easily expanded to a large
             number of subdivisions
                   Numerical techniques can be used to analyse th
                   resulting coupled systems

USPAS June 2007, Superconducting accelerator magnets                Magnet Protection 16.28
                                     Protection via subdivision:
                                            Using diodes
      Diodes are nonlinear circuit elements that carry current only
      when subjected to voltages greater than a threshhold
      voltage Vth




USPAS June 2007, Superconducting accelerator magnets               Magnet Protection 16.29
                                Active protection using heaters

      The passive methods discussed so far require a balance
      between the anticipated normal zone growth and the
      resistance of the secondary or shunts
             Fast response may not be compatible with the required heating or
             with usual operating ramps
      An alternative is to provide active heaters on the coil
             Advantages:
                   Full design control
                           Ramp time
                           Minimization of thermal diffusion time
                           Placement (e.g. high field region) for maximum efficiency
                   No heat imposed during ramps
             Disadvantages
                   Active – require detection and triggering
                   Added component in magnet design – space issues
USPAS June 2007, Superconducting accelerator magnets                                   Magnet Protection 16.30
                                                       Heater design

      Heaters are typically thin strips of stainless steel
      Heaters should:
             encompass multiple turns
             encompass a full cable twist pitch of each turn
             Be as close to conductor as possible
                   Minimize thermal diffusion time (limiting time constant)
             Provide sufficient dielectric strength




USPAS June 2007, Superconducting accelerator magnets                          Magnet Protection 16.31
                                                       Example: LHC

      Real accelerator systems combine many of the previous
      techniques to provide reliable and fast protection




USPAS June 2007, Superconducting accelerator magnets                  Magnet Protection 16.32
                                                       Summary

      Protection systems are a key component of every magnet
      A few basic time constants can provide quick insight into the protection
      regime that may be necessary
      Based on the coil parameters, a designer must choose one or more
      protection strategies that minimizes risk
      Passive methods are the most reliable systems, but all energy is dumped
      in the cryogenic region
      Active external dump resistors deposit energy at room temperature,
      saving cryogenic power requirements, but result in high voltages and
      dependence on fast detection
      Passive methods, such as using a coupled secondary or magnet
      sudivision, can substantially reduce the magnet time constant, but a
      heat load is incurred with any dB/dt
      Active methods incorporating quench heaters require fast quench
      detection, but are required for high-current density magnets typical of
      state-of-the-art accelerators


USPAS June 2007, Superconducting accelerator magnets              Magnet Protection 16.33

				
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