Measurement of the Electron Cloud Density in a Solenoid Field and a Quadrupole Field K. Kanazawa and H. Fukuma KEK June 2009 CTA09 1

Contents Principle of the estimation of the near beam electron cloud density with a retarding field analyzer (RFA). Electron cloud density in a solenoid field. Electron cloud density in a quadrupole magnet. Summary. Many thanks are due to: Y. Funakoshi, H. Koiso, K. Ohmi, K. Oide, M. Tobiyama, Y. Suetsugu, H. Hisamatsu and MELSC operation crew. 2

Principle of the estimation of the near beam electron cloud density with RFA 1. The Principle Assumption: High energy electrons that reach a chamber wall are produced from slow electrons near the beam through the interaction with a circulating bunch. Density = Electrons above a threshold energy per bunch Volume near the beam determined by the threshold and detector geometry 3

Principle of the estimation of the near beam electron cloud density with RFA 2. Calculation of the Volume Simulation Put electrons at rest on the grid of 0.1 mm by 0.1 mm in the x-y plane that stands right in front of the detector. Neglecting the initial energy of electrons is an approximation. Count the number of electrons that enter the detector within 6 ns (3 bucket space) after the interaction with a three dimensional bunch. The time limit of 6 ns is for the present operational pattern of KEKB LER. For other bunch patterns, this is an approximation. The bunch is longitudinally sliced into 100 pieces. Each slice kicks electrons according to the Bassetti-Erskine formula. Volume = No. of electrons  10 -8 m 2  detector length. 4

Given a solenoid field, only high energy electrons produced near the bunch can enter the groove and reach the detector behind it. (Energy range is determined geometrically.) With the help of simulation, the detector current is converted into the density near the beam. Electron cloud density in a solenoid field 1. Vacuum Chamber Design RFA type monitor used without solenoid field Monitor used with solenoid field Groove SR Detector 1 Detector 2 (S1) (S3) 94mm 5

Electron cloud density in a solenoid field 2. Inside of the Chamber groove Monitor used with a solenoid field is hidden The entrance of RFA used without a solenoid field Whole view Dimension of the solenoid 6

y[mm] x[mm] E[keV] x[mm] Starting points of electrons that enter the detector Energy range of the electrons Electron cloud density in a solenoid field 3. Simulation to find a Source Volume Only these electrons reach the detector. Beam Bunch size:  x = 0.434mm,  y = 0.061mm,  z = 6mm B = 50 G, N B = 7.5  Detector Energy threshold is geometrically given at about 1 keV. 7

N B = 7.50  points N B = 5.31  points N B = 3.13  points N B = 1.50  points Electron cloud density in a solenoid field 4. Simulation Results for Different N B -15mm < x,y <15mm 8

Electron cloud density in a solenoid field 5. Source Volume in a Solenoid Field of 50G. The volume is roughly proportional to the square of the bunch current. It is essentially determined by the energy threshold given geometrically. The volume for the new detector is a half of the graph. 9

Electron cloud density in a solenoid field 6. Discussion on the Measured Current Measured current with the old detector (above) always show a large difference between the detectors. To reject the effect of possible low energy electrons, a new detector with a grid is provided. The new detector shows the same tendency as the old detector (left). Both detector seem to have a background which is proportional to the total current. Collector +100 V 10

Electron cloud density in a solenoid field 7. Photon Background A plausible source of the background is a photo-electron current from the grid. It is proportional to the total beam current and independent of bunch pattern. It is larger in the detector 2 whose opening faces the surface directly illuminated by synchrotron radiation. If the grid is positively biased, photons on a collector will be measured as a positive current. This is actually so, though the ratio of the current is different from the negatively biased case. The effect of photon is also seen in the density estimation without a solenoid field at a low bunch current where S1 always shows higher value. SR Detector 1 Detector 2 S1 S3 11

Electron cloud density in a solenoid field 8. Cloud Density with a Solenoid Field The near beam cloud density is reduced by four or five orders of magnitude in a solenoid field of 50 G. Simulation tells the density is below 10 6 m -3. The background is subtracted. The estimated density becomes similar for both detectors. 12

Electron cloud density in a solenoid field 9. Cloud Density with a Solenoid Field for Different Bunch Patterns [4,200,4] 8 ns [4,100,8] 16 ns [4,200,3] 6 ns [8,100,2] 4 ns B = 0 G B = 50 G 13

Electron cloud density in a quadrupole magnet 1. Concept X-axis Detector In a quadruple magnetic field, electrons accelerated by a bunch along X-axis reach the detector. Electrons accelerated with small angle to X- axis moves spirally around X-axis losing their energy along X- axis to the spiral motion. Electrons with sufficient energy and direction close to X-axis reach the detector. With the help of simulation detector current is converted into the density near beam. Detector 2 Detector 1 SR Pole 92mm 14

Electron cloud density in a quadrupole magnet 2. Pictures Detector QA1RP Bore radius = m B’ = T/m Effective length = m 15

QA1RP:  x = 0.35 mm,  y = mm,  z = 6.0 mm B’ = 3.32 T/m N B = 7.5  Electron cloud density in a quadrupole magnet 3. Simulation to find a Source Volume x [mm] y [mm] Detector Bias = -1 keV. The big island is an expected source. Other small islands are unexpected. Detector Approximate calculation for a point bunch. The region is mainly limited by the detector bias. 16

N B = 7.50  points N B = 5.31  points N B = 3.13  points N B = 1.50  points Electron cloud density in a quadrupole magnet 4. Simulation Results for Different N B -20mm < x,y < 20mm 17

Electron cloud density in a quadrupole magnet 5. Source Volume in QA1RP The volume is roughly proportional to the square of the bunch current. It is essentially determined by the energy threshold given by the detector bias. 18

Electron cloud density in a quadrupole magnet 6. Cloud Density in QA1RP The estimated density of the order of m -3 in QA1RP is consistent with the simulation. Two RFA’s gave different estimation. The behavior of the density against the bunch current is qualitatively similar. The difference in two detectors is sensitive to COD. Simulation by CLOUDLAND Photon reflectivity: 0.3 Photo-electron yield: 0.1  MAX = 1.2 at 250 eV 19

Electron cloud density in a quadrupole magnet 7. Cloud Density in QA1RP with Different Bunch Patterns 20

Summary The near beam electron cloud density in a magnetic field was estimated with RFA based on the assumption that high energy electrons that hit a chamber wall are produced from slow electrons near the beam through the interaction with a circulating bunch. The measured current in a solenoid field is considered to contain a photo-electron current from the grid of the detector as a background. The background is subtracted when the cloud density is estimated. The near beam electron cloud is reduced by four or five orders of magnitude in a solenoid field of 50 G. The estimated density in a quadrupole magnet lies in the same order as the value obtained by simulation. The difference of the density between two detectors in a quadrupole field is sensitive to COD. 21