SC-MAG-650 
                                                                        
                                                  
A Training Mechanism within Superconducting Magnets Made from Multi-Strand Cables
This was supported by the
Director, Office of Energy Research, Office of High Energy and Nuclear
Physics, High Energy Physics Division, U. S. Department of Energy, under
Contract No. DE-AC03--76SF098.
Shlomo Caspi and Alan Lietzke
Lawrence Berkeley National Laboratory
University Of California
Berkeley, CA 94720
s_caspi@lbl.gov

Abstract

Recent LHC IR quadrupole training results motivated an improved understanding, and quantification of a quench-triggering mechanism that was proposed and tested during LBNL's D19 magnet program in 1995.  

The mechanism depends upon stick-slip changes in cable dimensions during magnet excitation.  It is expected to be have the largest impact at those locations within the magnet where the following four conditions are simultaneously satisfied: 1) magnet assembly procedures have axially compressed the cable, 2) transverse loading has locked the strands in their axially compressed locations, 3) subsequent Lorentz loading tensions the cable, while 4) azimuthal Lorentz unloading allows the strands to slip.  In long multi-pole magnet coils these conditions are most likely to occur on the inner-most (pole) turn, in the transition region between the straight section and the end-region. The mechanism is believed to be best weakened by magnet assembly procedures that ensure that all strands are tightly packed, in positions similar to those produced during Lorentz tensioning of the cable.

A simple 2-D model allows estimates of the stress/strain conditions within this region, when subjected to various coil conditions: wound, assembled, collared, cooled, and energized.  Some results are presented for Fermi LHC quadrupole prototypes.

Prologue

The transverse dimensions of a "Rutherford" cable are strongly dependent upon its axial stress state (most.  dramatically observed by axially compressing an unwrapped segment). Although wrapping insulation over the cable substantially stiffens the cable, the stress/strain relationship of a compressed cable is expected to be considerably softer than a tensioned cable; and a Kapton wrapped cable is expected to be softer than a glass-wrapped cable.  

Cable compression is expected to occur when the pole-piece, which opposed the accumulated winding tension, is removed after coil curing.  The stress redistribution puts neutral portions of the coil (e.g. wedges, and insulation) under compression, while reducing the tension elsewhere. 

ofto the extent that the tcomposed of a number of parallel strands that are twisted under tension, and folded over themselves under high pressure in a manner to make a flat ribbon-like cable.  Under normal conditions, the cabled strands are fairly tightly packed, lying in two layers, with a characteristic twist-pitch relative to the length of the cable.  The high cabling pressure causes a variety of strand deformations ("saddles", "knuckles", and "sockets") that interlock in a manner to maintain the cable's ribbon-like shape over a limited range of cable tension and compression.  The cable is usually wrapped with some thin insulation in a manner to provide turn-to-turn insulation, and help maintain the cable's structural integrity during the coil-winding process.  A thin layer of thermal-setting glue is on the non-conductor side of the tape, which will subsequently be used to "glue" the coil's turns together in a manner to maintain coil integrity during subsequent magnet assembly. 

Coils are created by winding cable around a form ("pole-piece") that has the appropriate shape and size that is needed to produce the desired magnetic field characteristics.  The cable's winding tension is chosen to provide reproducible coil characteristics (shape, size, insulation integrity). It is often close to the original cabling tension because the most repeatable, minimum cable dimension occurs when the interlocking saddles and knuckle/socket sets are near the positions in which they were cabled.   The internal stress distribution is always consistent with a mechanical equilibrium. In long magnets, the winding tension is primarily reacted by the pole-spool's "nose" or "end" pieces.  With a stiff pole, the force accumulation is proportional to the number of turns.  In layer #1 of the FermiLab quad there are 14 turns @ 75 lb.turn, producing a maximum pole force of 2100 lb. (75x14x2). 

The coils are normally "cured" after winding by subjecting them to a temperature that activates the aforementioned inter-turn thermal-setting glue.  Curing is done under a pressure, and within a form, that insures the proper coil shape, size, or modulus, with good adhesion between turns.  The curing process is not expected to significantly change the stress state of the coil system.  However, in preparation for collaring, a crutial step occurs after curing --- the pole key is removed from the coil, i.e., the force, previously supplied by the pole key (2100 lb for FermiLab's LHC quad), is removed.  The coilstress redistributes itself, according to the new boundary conditions:  Portions of the coil that were neutral (e.g., wedges, insulation) must go into axial compression.  Portions that were in tension (e.g. cable), either reduce their tension, or go into compression.  The details of the stress re-distribution are expected to depend upon a variety of parameters: the relative stiffness of the wedges, the shear modulus of the insulation and insulator-to-insulator bonds obtained during "curing", and the relative stiffness of the insulator wrap that resists changes in cable dimension. 

In most accelerator-quality magnets, wedges are present (to provide the desired field quality). Cable tension can be maintained only to the extent that the wedges go into compression.  Gaps in straight-section wedges are expected to reduce until they are either closed, or the net cable tension is removed.  The ends are a different matter.  Any transfer of the outer turn tension to the inner turns, requires that the inner turns go into compression.  This is the normal case in most accelerator magnets, since the end-spacers rarely have a good fit to the wedges (in the interest of having compact ends during the winding process).  This compression of the inner turns  (Fig. 1) is expected to propagate into the straight section to the extent permitted by the shear modulous of the inter-turn insulation system.  The inner turn is expected to have the greatest compressional stress

Hence, the following changes are expected when the pole is removed from "normal" accelerator magnet coils: 1) the coil shortens (consistent with the reduction in cable tension, 2) the transverse coil size increases (as the interlocking cabling-saddles ride higher up their sides, thereby thickening and widening each cable), and 3) the ends bulge outward (due to a force distribution that attempts to straighten each end). Furthermore, since plastic is often the primary means of maintaining a coil's non-zero stress distribution, creep in the above parameters can be expected to continue for some time.

Cured coil with pole key in (top), and with pole key removed (bottom).

Small changes in cable tension cause small twisting and translational displacements of the strands with respect to each other as the interlocking saddles and knuckle/socket sets adjust to the change in axial stress state.  Increasing the cable tension packs the strands more tightly, while axial compression produces a very fluffy, loose, spring-like structure, with space between the strands. The effect of reducing, or reversing, the axial cable tension is most dramatically observed by axially compressing a short length of unwrapped cable: the strands separate, and the cable gets wider and thicker.  The insulation wrap is expected to resist this movement to the extent that it can maintain tension (around the cable) and compression (in the cable's axial direction). The "curing" glue is only on the side of the insulation facing away from the cable, leaving the cable relatively free to slide within.  The stress-strain curve around zero stress is expected  to look somewhat like the curve in Fig. 2. If the cable is supported on both sides by other cables or wedges, one can expect the compressive response to be slightly stiffer. Pole turns have no side support until they are collared.

A stress strain curve for a cable under axial tension and compression.

When the magnet is collared and placed under azimuthal compression (
direction) the compressed regions are left unaffected.

We point out again that what maintains the cable integrity is the
locking mechanisms between strands or the "knuckles". Under tension
strands interlock whereas under compression they simply move apart (Fig.
3). 
While under tension strands engage, however they separate under
compression.

Training

When the magnet is energized, end forces attempt to stretch it even if
the magnet is restrained by end plates. Turn to turn strain and motion
will still occur. When such forces increase, the degree of compression
(along the cables) near the ends will diminish and may eventually
disappear with the cable going into tension. The process may be enhanced
by the fact that while axial forces increase, prestress near the pole
and in the  direction decreases. The combined effect increases the
chances of strands within the pole turn to displace axially seeking a
new local equilibrium. It is conceivable that while this process occurs 
interlocking strands generate frictional heating and may quench the
magnet. Other sources such a very low azimuthal () prestress also
contribute to the training process, however we assume that the magnets
adequately pre-stressed.

Reduce Training

Based on what has been described it is obvious that in order to improve
magnet performance we need to eliminate the state of axial compression
near the ends. The obvious way to do that is not to remove the pole
keys. This however may not be possible when collars are used. We can
also consider splitting the collars by making the pole an integral part
of the coil never to be removed. The other choice is to STRETCH the
magnet, a process that is not simple but quite possible. We also
recommend to wind each coil with the highest possible tension and
gradually reduce the tension when each subsequent turn is wrapped on.

Evidence

So far the effect of longitudinal compression in cables on training was
given little attention. We list some of the limited evidence we have on
that: 
When LBL built its 17 m long SSC dipoles at BNL, it maintained constant
winding tension in the coil windings. After the magnets were cured and
the pole key removed the inner turns in the end region developed many
turn to turn shorts.
Tests on long SSC magnets proved that training is not length dependent
and is a "local" phenomenon.
In the early 90's LBNL has built a 1 m long SSC dipole (D19) with thin
elliptical collars. This magnet reached it short sample limit on its
first quench (central field of 7.6 T). This coil was stretched to its
original axial position. At 1.8 K the magnet reached 10 T after a series
of training quenches.
The KEK IR quads are now being tested for the effect of coil stretching
on training. By doing so A. Yamamoto has expressed his suspicion that
such a process may indeed improve the magnet performance.

Analysis

We have computed the stress in the windings near the ends of the Fermi
LHC quad, assuming:  
The coil is flat (as shown in Fig. 4) and is plain stress
The ends are circular (no straight section)
The windings and field are solenoid like.
Cable tension and temperature dependence included.
Azimuthal or tangential is along the cable direction. Radial refers to
the direction across turns or turn to turn.
 Computations were based on the report "Stress-Strain in Shells Under
Mechanical, Thermal, and Magnetic Loads" S. Caspi et al, SC-MAG-616,
March 1998. (postscript
http://supercon.lbl.gov/caspi/publication/stress_in_shells.ps ) 
Simulation of accelerator "end" coils as a solenoid.

The cable and the cross section geometry are that of the inner layer of
the Fermi LHC IR Quad (Fig. 5). 
LHC IR quad cross section
LHC IR quad --- top view of "end" region.

As each turn is wrapped with 75 lb. of tension inner turns loss some of
their tension. When the last turn (14) is wrapped, it is under 14 MPa of
tension while the inner turn (1) has reduced it tension to an average 4
MPa. The pole key is now compressed to ---27 MPa (Fig. 7 top). Removing
the pole key (Fig. 7 bottom), does not change the tension in the outer
turn, however all other turns reduce their tension and the inner most 6
turns go into tangential compression, reaching ---20 MPa in the inner
most turn. Reducing the temperature readjusts the stress distribution.
The outer most turn is now at 10 MPa of tension and the inner turn drops
to ---29 MPa of compression. Figures 8 and 9 show the corresponding
radial stress and displacements.

Azimuthal stress, along cable, showing wrapping with pole key in,
equilibrium after pole has been removed and cool down.
Turn to turn stress (across turns).
Displacements across turns.

If we now turn on the field (assuming it is solenoidal) and introduce
field and currents values that are typical to that of a first quench and
the short sample, the stress distribution will be modified to that shown
in Figures 10,11 and 12. During the first quench all turns are at 22 MPa
of tension, however at short sample the outer turn reaches 35 MPa and
the inner turn 65 MPa. In addition, as shown in Fig. 11, the stress
across turns (turn to turn) is not fully compressive, 6 turns near the
"nose" are now in tension.

Stress along turns including magnetic forces at the first quench level
and short sample.
Turn to turn pressure including magnetic forces.
Displacements

If we wish to readjust the force level in the "end" to match the level
that corresponds to the initial tension, first quench and final short
sample, we shall have to apply on each end a corresponding axial force
of 1350 lb., 1975 lb. and 3950 lb. (Fig. 13).

Pressurizing the pole key area to achieve an equivalent cable tension as
with Lorentz forces.