1. Enhancement of Single Stretched Wire Measurements of LHC Short Straight Sections Guy Deferne, Nikolay Smirnov, CERN Joe DiMarco, FNAL 14th International Magnetic Measurement Workshop 26-29 September 2005, Geneva, Switzerland

2. 28.09.2005IMMW142 Content  Introduction – The Single Stretched Wire (SSW) at CERN  Part I - Roll Angle Offset Calibration  Introduction  Case of a centered magnet  Case of a non-centered magnet  Example of calibration  Part II - Integrated Strength (Gdl) Measurements For more details, please see the presentation of N. Smirnov et al, « Focusing strength measurements of the main quadrupoles for the LHC », submitted at the MT19 Conference, 2005)  Introduction  Shape of the wire  Gdl Measurement procedure  Magnetic properties of the wire  System performance  Conclusion

3. 28.09.2005IMMW143 The Single Stretched Wire (SSW) are the reference systems used for the integrated strength and field direction measurements –Three systems operational –All three are similar to the ones used at DESY and at FNAL One of the two stages System installed on a cold bench Introduction The SSW features used at CERN: Warm and cold integrated axis of MQ and associated correctors Integrated strength of MQ and MB at cold Warm and cold integrated roll angle of MQ, correctors and MB  Nearly 500 Short Straight Section (SSS) for the LHC.  All of them are an assembly of different magnets  10 % of those must be magnetically measured

4. 28.09.2005IMMW144 Roll angle offset calibration (1) Introduction  The field direction is one of the essential parameters of the measurement campaign  The SSW systems must be periodically calibrated in sense of roll angle in order to perform fast measurements that fulfill the requirements Two different type of calibration can be used, depending if the measured magnet is centered or not in between the stages Part I – Roll angle offset calibration

5. 28.09.2005IMMW145 Roll angle offset calibration (2) Stages are aligned w/r to gravity with 5µrad resolution Wyler inclinometers zAzA zBzB offset stageA offset stageB α gravity α field α gravity Stage A Magnet Stage B If z A =z B AND α field =α gravity (reference magnet), then Swapping stages Introducing the system offset in the calculation allows to perform absolute angle measurement without swapping the stages Case of a centered magnet If z A =z B, then Absolute field direction w/r to gravity: System offset:

6. 28.09.2005IMMW146 On cold benches, the magnet is NOT centered in between the stages Inside an SSS, the different magnets are located at different longitudinal positions Layout of the magnets inside an SSS Stage A Stage B MQ MSCB MO/MQT 2.94m 4.975m 6.849m 11.68m Roll angle offset calibration (3)Case of a non-centered magnet (1)

7. 28.09.2005IMMW147 Roll angle offset calibration (4) Simply swapping the two stages as for a regular absolute offset calibration is not sufficient; the variation of the offset along the longitudinal position must be taken into account During the calibration, one of the stage is placed closer to the magnet A stage B stage Reference quadrupole SSW stages installed on the calibration bench Case of a non-centered magnet (2) If z A ≠z B, then where:z is the distance from stage A to the magnet center and l is the distance between the stages

8. 28.09.2005IMMW148 Roll angle offset calibration (5) The roll angle offset parameter is updated for each type of magnet, in each SSW system. Example of calibration

9. 28.09.2005IMMW149 Integrated Strength (Gdl) (1) A second essential parameter of the measurement campaign is the integrated gradient (Gdl) of quadrupoles This is one of the most challenging magnetic parameters of the LHC magnets –Required absolute error (Magnetic measurement): 5[units] –Required repeatability (Magnetic measurement):< 5 [units] For the Stretched Wire Systems, this means an error on the wire positioning less than 2.5µm over 12m! Introduction Only a proper method and good properties of the wire can give results inside specifications Part II – Integrated Strength (Gdl) measurement

10. 28.09.2005IMMW1410 Integrated Strength (Gdl) (2)Shape of the wire (1) The position of the wire at the stages is known within 1 µm, but inside the magnet, the wire is deflected by magnetic forces and gravity Therefore, the weight of the wire and its magnetic properties must be taken into account. Magnetic forces Gravity Stretched wire Vertical position of the wire: Horizontal position of the wire: T is the wire tension w is the mass per unit of length F mag is the magnetic force. Where: Note: the sign of the force F mag depends on the magnetic properties of the wire and its location in the field with z is the longitudinal position w is the wire weight per unit of length G the gradient of the field D the wire displacement  is the wire susceptibility T is the wire tension Where: Possible solutions of (1): (1)

11. 28.09.2005IMMW1411 Note: Integrated Strength (Gdl) (3)Shape of the wire (2) Sag of the wire: As tension measurement is affected by friction problems and gauge accuracy, the SSW system measures the fundamental frequency of the wire, which includes its mechanical properties B stage A stage

12. 28.09.2005IMMW1412 Integrated Strength (Gdl) (4)Gdl measurement procedure Dependence of transfer function as a function of wire tension with CuBe wire 0.13mm diam The Gdl obtained from a horizontal movement, can be calculated from the linear fit of different wire tensions. The Gdl obtained from a vertical movement must be calculated from the parabolic fit of different wire tensions. The parabolic term of the polynomial expansion comes from the sag of the wire:, To cancel the effect of the magnetic forces, the value of the strength is calculated from the extrapolation of Gdl = f(1/f 2 ) at the interception of the axis, where 1/f 2  0 (infinite tension) Note:

13. 28.09.2005IMMW1413 Integrated Strength (Gdl) (5)Magnetic properties of the wire Four different wires have been tested: 1.  0.1mm CuBe wire from California Fine Wire Co, USA 2.  0.1mm Mg wire from California Fine Wire Co, USA 3.  0.13mm CuBe wire from Goodfellow Co, UK 4.Carbon fiber strand from Toho Tenaz Europe gmbh, type HTA5241 (5). (  0.078mm silicon carbide, type SCS-9A from Speciality Materials Co, USA) (Note: type 5. could not be magnetically tested because of its high rigidity) Wire 0.76kA5kA11.85kAχ CuBe 0.1mm30.420009480>0 Mg 0.1mm6.1 500 4977>0 CuBe 0.13mm 2.350 474<0 Multi filament Carbon strand --380<0 Slopes of strength for different types of wire in [T/s 2 ] CuBe Carbon fiber HTA5241 SCS-6 Silicon Carbide Different type of tested wire Note: if strength rises when tension increases, wire is diamagnetic If strength falls when tension increases, wire is paramagnetic

14. 28.09.2005IMMW1414 The error on the extrapolation is proportional to the slope The lower is the susceptibility, the smaller is the random error on Gdl Integrated Strength (Gdl) (6)System performance (1)     Gdl 1/T 1. Random error Typical random error vs Gdl Gdl stdev at interception point Total random error Contribution of the slope (magnetization of the wire) Qualification of two SSW systems Parameter/SSW UnitsSSW#1SSW#2 δ noise units*T210400 η slope units*T -3 2.5*10 -9 5*10 -9 Gdl lower acceptable limit (5units at one sigma) T4280 As Gdl at injection is 44T, its measurement can be performed only with certain statistic InjectionNominal Tolerance limit Dev(Gdl) [units]

15. 28.09.2005IMMW1415 Integrated Strength (Gdl) (7)System performance (2) 2. Systematic errors Estimated contribution Powering of the magnet:<0.1[units] Amplifier and integration:<0.1[units] Main field errors:<0.2[units] Stray field (on cold test benches):  2.3[units] Alignment of stages: <1[units] Wire susceptibility:<2[units] ____ Total (rms)<3.2[units ]  A cross calibration with a system that uses a different method of Gdl measurement could give a valuable confirmation of the systematic error of the SSW systems performances  The twin shafts and the automated scanner (both are rotating coils systems) used in SM18 cannot guaranty so far better than 20 [units] of absolute error  Thus an estimation of the all possible and known sources of systematic error is used to qualify the SSW systems at CERN

16. 28.09.2005IMMW1416 Conclusion A special method has been developed to measure the integrated strength (Gdl) of the LHC MQ with an accuracy within the specification (even though a statistical study is required at injection field) Gdl measurements: AbsoluteRandom Error specifications:5 [units] 5 [units] Error obtained:est. <3.2[units]<5[units] Different wires have been tested for their magnetic and mechanical properties and one type, the 0.13mm diam. CuBe from Goodfellow Ltd, has been chosen for the LHC measurements As we have shown that not any wire can be used for Gdl measurements, the search for wires with a lower susceptibility will continue A procedure has been developed to calibrate the roll angle offset of the Single Stretched Wire systems as a function of the magnet longitudinal position. This allows to measure the field angle w/r to gravity of the main quadrupoles and correctors magnets installed in an Short Straight Section without any swapping of the system stages. Roll Angle Calibration Integrated Strength