# Presentation: 005740

## Main Effects of TEL Magnets on p & pbar Beams

-  TEL Magnets
-   Coupling Coefficients
-   Maximum Orbit Changes
-   Dispersion Changes
-   Effects of Quad- and Sext- Component
-   Focal Length of the Main Solenoid
-   Corrections
-   Impedance Estimations
-   Machine Study Observation

- X. Zhang                                                BBC Project Review

## Introduction

- X. Zhang                                                BBC Project Review

## Solenoid Magnets Combination 

**Solenoid Magnets Combination **

- X. Zhang                                                BBC Project Review

## Coupling Coefficient of Main SC Solenoid

- Define Coupling Coefficient
-      For single Solenoid:
-     where *B**s* is magnetic field strength, *L**e* the effective magnet length and *B**** *the beam magnetic rigidity.

- X. Zhang                                                BBC Project Review

## Dipole Kicks of Solenoid Magnets

- Bending Angle of Gun-Solenoid Line and Solenoid-Collector Line
-      Kick Angle
- Orbit Displacement
-      Bending angle canceled each other of the Gun-Solenoid-Collector system, result in a net orbit displacement
-       *L* is the length of the main solenoid.

- X. Zhang                                                BBC Project Review

## Residual Kick Angle

- Pessimistic Estimation
-      Gun-Solenoid Line:
-       Solenoid-Collector Line:
- Maximum Orbit Change

- X. Zhang                                                BBC Project Review

## Effects of Dipole Correctors

- Kick Angle of the Dipole Correctors
-        Maximum Nominal Integral Field
-        Long Dipole at:   0.36 Tm,
-                     Can Displace *e**-* Beam: 100 mm at Bs = 3.5 T
-        Short Dipole at:   0.1   Tm,
-                      Can Displace *e**-* Beam:  29 mm at Bs = 3.5 T
- Operated like a 3-bump

- X. Zhang                                                BBC Project Review

## Dispersion Changes

-            Before Solenoid Put in:
-                        *D**x* = 2.5 m, *D**y* = 0.082 m
-            After Solenoid Put in:
*                           **D**x* = 2.5 m, *D**y* = 0.058 m

- X. Zhang                                                BBC Project Review

## Gradient Effects

- Tune Changes at the Maximum Bs Field:
-              8.510-4    at 150 GeV
-              1.310-4    at  1 Tev

- X. Zhang                                                BBC Project Review

## Gradient Effects

- Coupling Due to Skew Gradient:
-      *C**q*  5.6%     at   150 GeV
-             0.9%     at   1 TeV

- X. Zhang                                                BBC Project Review

## Focal Length of the Main Solenoid

-        Maximum Tune Change < 0.001
-        at 150 GeV ( *β**x* = 116 m )

- X. Zhang                                                BBC Project Review

## Chromaticity

- At *B**s*=6.5 T and 1 TeV

- X. Zhang                                                BBC Project Review

## Overall Estimations at Bs = 6.5 T

- Two end compensate each other
-    1.  Tune:
-          Gradient effect 20% + Solenoid effect
-       8.510-4 20%  + 1.110-3 1.210-3  (150GeV)
-          1.310-4 20%  + 2.410-5 0.510-4  (980GeV)
-    2.  Coupling:
-        Gradient effect 20% + Solenoid effect
-       5.6% 20%  + 0.53%  1.7%   (150GeV)
-          0.9% 20%  + 0.1%   0.3%  (980GeV)
-    3.  Orbit:   < 0.07 mm

- X. Zhang                                                BBC Project Review

## Corrections

- TEL Phase: *μ**x* = 16.94, *μ**y* = 16.94
- Coupling Correction:
-        *TSQA0 *(17.0),* TSQA4 *(20.3),* TSQB0, *
*         **TSQD0 *(6.7, 7.3),* TSQ,   TSQE0 *(10.5)
- Local Kick Angle Corrections:
-          *VDF47 *(*μ**y* = 16.85)*, VDF49 *(*μ**y* = 16.97)
*         **HDF46 *(*μ**x* = 16.742)*, HDF48 *(*μ**x* = 16.931)
- Global Orbit Correction

- X. Zhang                                                BBC Project Review

## Observations

- At *B**s* = 6 T, 150 GeV  *(J. Annala)*
-      (.5748, .5854)  (.5744,  .5874) with TEL magnets on.
-      Tune separation increased about 23%
-       T:SQ  -3.05  -3.065, brought tune separation to 0.0038
- At *B**s* = 3.5 T, 980 GeV
-     (.5717, .5789)  (.5713,  .5792) with TEL magnets on.
-            = 0.0072        = 0.0079    tune separation
-        RMS Orbit change due to TEL  (0.8, 1.2) mm

- X. Zhang                                                BBC Project Review

## Impedance Estimation

- A. Burov: "careless" limit Z/n = 0.07 Ω
- For D = 6 cm hole, Z/n < 0.1 mΩ
- For 10 long gap (inexistent actually) in optical diffraction model Z/n < 0.1 Ω
- At proton intensity of 7.71010, the measured signal at all HV electrodes of the TEL are:
-      #9 29.4 V #10 20.1 V #11 1.2 V #12 18.0 V #13 22.1 V #14 45.4 V #15 14.0 V #16 7.5 V #17 11.0 V #18 4.7 V
- Pick-up signals are of the order of 15 V peak-to-peak
- Detailed simulation might be needed.

- X. Zhang                                                BBC Project Review

## Conclusion

- No Disastrous Effects Found
- More Machine Study Time Needed for Fine Tune of the System.

- X. Zhang                                                BBC Project Review