| Acknowledgements |
|
xv | |
| Nomenclature |
|
xvii | |
| Introduction |
|
1 | (2) |
|
|
| References |
|
3 | (2) |
|
|
|
5 | (24) |
|
|
|
|
|
5 | (1) |
|
1.2 Vacuum Specification for Particle Accelerators |
|
|
6 | (7) |
|
1.2.1 Why Particle Accelerators Need Vacuum? |
|
|
6 | (2) |
|
1.2.2 Problems Associated with Beam-Gas Interaction |
|
|
8 | (1) |
|
1.2.2.1 Beam Particle Loss |
|
|
8 | (1) |
|
1.2.2.2 Background Noise in Detectors |
|
|
8 | (1) |
|
1.2.2.3 Residual Gas Ionisation and Related Problems |
|
|
9 | (1) |
|
1.2.2.4 Contamination of Sensitive Surfaces |
|
|
9 | (1) |
|
1.2.2.5 Safety and Radiation Damage of Instruments |
|
|
10 | (1) |
|
1.2.3 Vacuum Specifications |
|
|
11 | (1) |
|
1.2.4 How Vacuum Chamber Affects the Beam Properties |
|
|
12 | (1) |
|
1.3 First Considerations Before Starting Vacuum System Design |
|
|
13 | (7) |
|
|
|
13 | (1) |
|
|
|
14 | (1) |
|
1.3.3 Beam Aperture and Vacuum Chamber Cross Section |
|
|
15 | (1) |
|
1.3.3.1 Required Mechanical Aperture |
|
|
15 | (2) |
|
|
|
17 | (1) |
|
1.3.3.3 Mechanical Engineering |
|
|
17 | (1) |
|
1.3.3.4 Other Factors Limiting a Maximum Size of Beam Vacuum Chamber |
|
|
17 | (1) |
|
1.3.4 Vacuum Chamber Cross Sections and Preliminary Mechanical Layout |
|
|
18 | (1) |
|
1.3.5 Possible Pumping Layouts |
|
|
19 | (1) |
|
1.4 First and Very Rough Estimations |
|
|
20 | (2) |
|
1.5 First Run of an Accurate Vacuum Modelling |
|
|
22 | (1) |
|
1.6 Towards the Final Design |
|
|
22 | (3) |
|
|
|
25 | (1) |
|
|
|
25 | (4) |
|
2 Synchrotron Radiation in Particle Accelerators |
|
|
29 | (32) |
|
|
|
2.1 Emission of a Charged Particle in a Magnetic Field |
|
|
29 | (3) |
|
2.1.1 Radiated Energy Density and Power Density |
|
|
31 | (1) |
|
|
|
32 | (1) |
|
|
|
32 | (10) |
|
2.2.1 Emission Duration and Critical Energy |
|
|
33 | (1) |
|
|
|
34 | (3) |
|
2.2.3 Vertical Angular Distribution of Photon Flux |
|
|
37 | (2) |
|
|
|
39 | (2) |
|
2.2.5 Vertical Angular Distribution of Power |
|
|
41 | (1) |
|
|
|
42 | (1) |
|
2.4 SR from Insertion Devices |
|
|
43 | (12) |
|
2.4.1 Motion of Charged Particles Inside a Planar Insertion Device |
|
|
44 | (1) |
|
2.4.2 Resonance Wavelength |
|
|
45 | (1) |
|
2.4.3 Radiation from Undulators and Wigglers |
|
|
46 | (5) |
|
2.4.4 Angular Aperture of ID at Resonant Wavelength |
|
|
51 | (1) |
|
2.4.5 Estimation of Power Distribution Radiated in a Wiggler |
|
|
52 | (2) |
|
2.4.6 Estimation of the Power Collected by Simple Geometry Aperture |
|
|
54 | (1) |
|
2.4.7 Method for Estimation Absorbed Power on the Complex Shapes |
|
|
54 | (1) |
|
2.5 Software Dedicated to Evaluation of the Photon Flux and Power Distribution from the Insertion Devices |
|
|
55 | (4) |
|
|
|
56 | (1) |
|
2.5.2 Synchrotron Radiation Workshop (SRW) |
|
|
56 | (1) |
|
|
|
57 | (1) |
|
|
|
58 | (1) |
|
|
|
59 | (1) |
|
|
|
59 | (1) |
|
|
|
60 | (1) |
|
|
|
60 | (1) |
|
3 Interaction Between SR and Vacuum Chamber Walls |
|
|
61 | (18) |
|
|
|
|
|
|
|
61 | (8) |
|
3.2 Photoelectron Production |
|
|
69 | (7) |
|
3.2.1 Total Photoelectron Yield |
|
|
69 | (3) |
|
3.2.2 Effect of the Photon Energy |
|
|
72 | (4) |
|
3.2.3 Effect of the Incidence Angle |
|
|
76 | (1) |
|
|
|
76 | (3) |
|
4 Sources of Gas in an Accelerator Vacuum Chamber |
|
|
79 | (96) |
|
|
|
|
|
4.1 Residual Gases in Vacuum Chamber |
|
|
79 | (2) |
|
4.2 Materials Used for and in Vacuum Chambers and Built-in Elements |
|
|
81 | (6) |
|
|
|
82 | (1) |
|
|
|
83 | (1) |
|
4.2.3 Copper and Its Alloys |
|
|
84 | (1) |
|
4.2.4 Titanium and Its Alloys |
|
|
85 | (1) |
|
|
|
85 | (1) |
|
4.2.6 Other Vacuum Materials |
|
|
86 | (1) |
|
|
|
87 | (15) |
|
4.3.1 Thermal Outgassing Mechanism During Pumping |
|
|
88 | (1) |
|
4.3.2 Equilibrium Pressure |
|
|
89 | (2) |
|
|
|
91 | (2) |
|
4.3.4 Thermal Outgassing Rate of Materials |
|
|
93 | (4) |
|
4.3.5 Outgassing Rate Measurements |
|
|
97 | (1) |
|
4.3.5.1 Throughput Method |
|
|
97 | (1) |
|
4.3.5.2 Conductance Modulation Method |
|
|
98 | (1) |
|
|
|
98 | (1) |
|
4.3.5.4 Gas Accumulation Method |
|
|
99 | (1) |
|
4.3.6 Thermal Desorption Spectroscopy |
|
|
100 | (2) |
|
4.4 Surface Treatments to Reduce Outgassing |
|
|
102 | (7) |
|
|
|
102 | (3) |
|
|
|
105 | (1) |
|
|
|
106 | (1) |
|
|
|
106 | (2) |
|
|
|
108 | (1) |
|
4.4.5.1 Coating the Surface by Thin Films of Material with Low Hydrogen Permeability and Low Outgassing |
|
|
108 | (1) |
|
4.4.5.2 Coating the Surface by Thin Film of Getter Materials |
|
|
108 | (1) |
|
4.5 Electron-Stimulated Desorption |
|
|
109 | (19) |
|
4.5.1 ESD Definition and ESD Facilities |
|
|
109 | (3) |
|
4.5.2 ESD for Different Materials as a Function of Dose |
|
|
112 | (1) |
|
4.5.3 ESD as a Function of Amount of Desorbed Gas |
|
|
113 | (1) |
|
4.5.4 Effect of Pumping Duration |
|
|
114 | (5) |
|
4.5.5 ESD as a Function of Electron Energy |
|
|
119 | (3) |
|
4.5.6 Effect of Bakeout on ESD |
|
|
122 | (1) |
|
4.5.7 Effectiveness of Surface Polishing and Vacuum Firing on ESD |
|
|
123 | (2) |
|
4.5.8 A Role of Oxide Layer on Copper |
|
|
125 | (1) |
|
4.5.9 Effect of Surface Treatment |
|
|
125 | (1) |
|
4.5.10 Effect of Vacuum Chamber Temperature |
|
|
125 | (3) |
|
4.6 Photon-Stimulated Desorption |
|
|
128 | (27) |
|
4.6.1 PSD Definition and PSD Facilities |
|
|
128 | (3) |
|
4.6.2 PSD as a Function of Dose |
|
|
131 | (1) |
|
4.6.3 PSD for Different Materials |
|
|
131 | (4) |
|
4.6.4 PSD as a Function of Amount of Desorbed Gas |
|
|
135 | (1) |
|
4.6.5 PSD as a Function of Critical Energy of SR |
|
|
136 | (1) |
|
|
|
137 | (3) |
|
4.6.7 Effect of Vacuum Chamber Temperature |
|
|
140 | (2) |
|
4.6.8 Effect of Incident Angle |
|
|
142 | (2) |
|
|
|
144 | (1) |
|
4.6.10 How to Use the PSD Yield Data |
|
|
145 | (1) |
|
4.6.10.1 Scaling the Photon Dose |
|
|
145 | (1) |
|
4.6.10.2 Synchrotron Radiation from Dipole Magnets |
|
|
145 | (3) |
|
4.6.10.3 PSD Yield and Flux as a Function of Distance from a Dipole Magnet |
|
|
148 | (3) |
|
4.6.10.4 PSD from a Lump SR Absorber |
|
|
151 | (2) |
|
4.6.10.5 Combining PSD from Distributed and Lump SR Absorbers |
|
|
153 | (2) |
|
4.7 Ion-Stimulated Desorption |
|
|
155 | (11) |
|
4.7.1 ISD Definition and ISD Facilities |
|
|
155 | (1) |
|
4.7.2 ISD as a Function of Dose |
|
|
156 | (2) |
|
4.7.3 ISD Yield as a Function of Ion Energy |
|
|
158 | (1) |
|
4.7.4 ISD Yield as a Function of Ion Mass |
|
|
159 | (1) |
|
4.7.5 ISD for Different Materials |
|
|
160 | (1) |
|
4.7.6 Effect of Bakeout and Argon Discharge Cleaning |
|
|
161 | (1) |
|
|
|
161 | (1) |
|
4.7.8 ISD Yield as a Function of Temperature |
|
|
161 | (2) |
|
4.7.9 ISD Yields for Condensed Gases |
|
|
163 | (3) |
|
|
|
166 | (1) |
|
|
|
166 | (9) |
|
5 Non-evaporable Getter (NEG)-Coated Vacuum Chamber |
|
|
175 | (40) |
|
|
|
5.1 Two Concepts of the Ideal Vacuum Chamber |
|
|
175 | (2) |
|
|
|
177 | (2) |
|
|
|
179 | (2) |
|
5.4 NEG Film Characterisation |
|
|
181 | (1) |
|
5.5 NEG Coating Activation Procedure |
|
|
182 | (6) |
|
5.6 NEG Coating Pumping Properties |
|
|
188 | (5) |
|
5.6.1 NEG Coating Pumping Optimisation at CERN |
|
|
188 | (2) |
|
5.6.2 NEG Coating Pumping Optimisation at ASTeC |
|
|
190 | (3) |
|
|
|
193 | (2) |
|
5.8 Ultimate Pressure in NEG-Coated Vacuum Chambers |
|
|
195 | (1) |
|
5.9 NEG-Coated Vacuum Chamber Under SR |
|
|
196 | (4) |
|
5.10 Reducing PSD/ESD from NEG Coating |
|
|
200 | (4) |
|
5.10.1 Initial Considerations |
|
|
200 | (1) |
|
5.10.2 ESD from Vacuum Chamber Coated with Columnar and Dense NEG Films |
|
|
201 | (1) |
|
|
|
202 | (2) |
|
5.10.4 Vacuum Firing Before NEG Deposition |
|
|
204 | (1) |
|
5.11 ESD as a Function of Electron Energy |
|
|
204 | (1) |
|
5.12 PEY and SEY from NEG Coating |
|
|
204 | (2) |
|
5.13 NEG Coating Surface Resistance |
|
|
206 | (1) |
|
5.14 NEG at Low Temperature |
|
|
207 | (1) |
|
5.15 Main NEG Coating Benefits |
|
|
207 | (1) |
|
5.16 Use of NEG-Coated Vacuum Chambers |
|
|
208 | (1) |
|
|
|
209 | (6) |
|
6 Vacuum System Modelling |
|
|
215 | (54) |
|
|
|
6.1 A Few Highlights from Vacuum Gas Dynamics |
|
|
215 | (13) |
|
6.1.1 Gas in a Closed Volume |
|
|
216 | (1) |
|
6.1.1.1 Gas Density and Pressure |
|
|
216 | (1) |
|
6.1.1.2 Amount of Gas and Gas Flow |
|
|
217 | (1) |
|
6.1.2 Total Pressure and Partial Pressure |
|
|
218 | (1) |
|
6.1.3 Velocity of Gas Molecules |
|
|
218 | (2) |
|
6.1.4 Gas Flow Rate Regimes |
|
|
220 | (1) |
|
6.1.5 Pumping Characteristics |
|
|
221 | (2) |
|
6.1.6 Vacuum System with a Pump |
|
|
223 | (1) |
|
|
|
223 | (1) |
|
|
|
224 | (1) |
|
6.1.7.2 Vacuum Conductance of Long Tubes |
|
|
224 | (1) |
|
6.1.7.3 Vacuum Conductance of Short Tubes |
|
|
225 | (1) |
|
6.1.7.4 Serial and Parallel Connections of Vacuum Tubes |
|
|
226 | (1) |
|
6.1.8 Effective Pumping Speed |
|
|
226 | (2) |
|
6.2 One-Dimensional Approach in Modelling Accelerator Vacuum Systems |
|
|
228 | (17) |
|
6.2.1 A Gas Diffusion Model |
|
|
229 | (2) |
|
6.2.2 A Section of Accelerator Vacuum Chamber in a Gas Diffusion Model |
|
|
231 | (1) |
|
6.2.3 Boundary Conditions |
|
|
232 | (6) |
|
6.2.4 Global and Local Coordinates for Each Element |
|
|
238 | (2) |
|
|
|
240 | (1) |
|
6.2.6 A Few Practical Formulas |
|
|
241 | (1) |
|
6.2.6.1 Gas Injection into a Tubular Vacuum Chamber |
|
|
241 | (1) |
|
6.2.6.2 Vacuum Chamber with Known Pumping Speed at the Ends |
|
|
241 | (3) |
|
6.2.6.3 Vacuum Chamber with Known Pressures at the Ends |
|
|
244 | (1) |
|
6.3 Three-Dimensional Modelling: Test Particle Monte Carlo |
|
|
245 | (12) |
|
|
|
245 | (1) |
|
6.3.2 A Vacuum Chamber in the TPMC Model |
|
|
246 | (1) |
|
|
|
246 | (2) |
|
|
|
248 | (1) |
|
|
|
248 | (2) |
|
6.3.4.2 Gas Density and Pressure |
|
|
250 | (1) |
|
6.3.4.3 Transmission Probability and Vacuum Conductance |
|
|
250 | (1) |
|
6.3.4.4 Pump-Effective Capture Coefficient |
|
|
251 | (1) |
|
6.3.4.5 Effect of Temperature and Mass of Molecules |
|
|
251 | (1) |
|
6.3.5 What Can Be Done with TPMC Results? |
|
|
251 | (1) |
|
6.3.5.1 A Direct Model with a Defined Set of Parameters |
|
|
252 | (1) |
|
6.3.5.2 Models with Variable Parameters |
|
|
253 | (3) |
|
6.3.6 TPMC Result Accuracy |
|
|
256 | (1) |
|
6.4 Combining One-Dimensional and Three-Dimensional Approaches in Optimising the UHV Pumping System |
|
|
257 | (3) |
|
6.4.1 Comparison of Two Methods |
|
|
257 | (1) |
|
6.4.2 Combining of Two Methods |
|
|
258 | (2) |
|
6.5 Molecular Beaming Effect |
|
|
260 | (5) |
|
|
|
265 | (2) |
|
|
|
265 | (1) |
|
6.B Modelling a Turbo-Molecular Pump |
|
|
266 | (1) |
|
|
|
267 | (1) |
|
|
|
267 | (2) |
|
7 Vacuum Chamber at Cryogenic Temperatures |
|
|
269 | (37) |
|
|
|
|
|
|
|
7.1 Pressure and Gas Density |
|
|
269 | (3) |
|
7.2 Equilibrium Pressure: Isotherms |
|
|
272 | (17) |
|
|
|
273 | (6) |
|
|
|
279 | (2) |
|
7.2.3 Physisorption on Gas Condensates |
|
|
281 | (1) |
|
7.2.4 Temperature Dependence of the H2 Isotherms |
|
|
282 | (4) |
|
7.2.5 Choice of Operating Temperature for Cryogenic Vacuum Systems |
|
|
286 | (3) |
|
7.3 Gas Dynamics Model of Cryogenic Vacuum Chamber Irradiated by SR |
|
|
289 | (11) |
|
7.3.1 Infinitely Long Vacuum Chamber Solution |
|
|
291 | (1) |
|
7.3.1.1 Vacuum Chamber Without a Beam Screen |
|
|
292 | (1) |
|
7.3.1.2 Vacuum Chamber with Holes in the Beam Screen |
|
|
292 | (2) |
|
7.3.2 Short Vacuum Chamber Solution |
|
|
294 | (2) |
|
7.3.2.1 Solution for a Short Vacuum Chamber with a Given Pressure at the Ends |
|
|
296 | (2) |
|
7.3.2.2 Solution for a Short Vacuum Chamber with a Given Pumping Speed at the Ends |
|
|
298 | (2) |
|
7.4 Experimental Data on PSD from Cryogenic Surface |
|
|
300 | (6) |
|
7.4.1 Experimental Facility for Studying PSD at Cryogenic Temperatures |
|
|
301 | (1) |
|
7.4.2 Discovery of Secondary PSD |
|
|
301 | (5) |
|
7 A3 Calculation of the Desorption Yields from Experimental Data |
|
|
306 | (43) |
|
|
|
308 | (2) |
|
7.4.5 Secondary PSD Yields |
|
|
310 | (2) |
|
7.4.6 Photon-Induced Molecular Cracking of Cryosorbed Gas |
|
|
312 | (1) |
|
7.4.6.1 Experimental Measurements |
|
|
312 | (3) |
|
7.4.6.2 How to Include Cracking into the Model |
|
|
315 | (1) |
|
|
|
316 | (2) |
|
7.4.7 Temperature of Desorbed Gas |
|
|
318 | (3) |
|
7.5 In-Depth Studies with COLDEX |
|
|
321 | (10) |
|
7.5.1 COLDEX Experimental Facility |
|
|
321 | (3) |
|
7.5.2 PSD of Cu as a Function of Temperature |
|
|
324 | (1) |
|
7.5.3 Secondary PSD Yields |
|
|
325 | (1) |
|
7.5.4 PSD of a BS with Sawtooth for Lowering Photon Reflectivity and PEY |
|
|
326 | (2) |
|
|
|
328 | (1) |
|
7.5.6 Temperature Oscillations |
|
|
329 | (2) |
|
7.6 Cryosorbers for the Beam Screen at 4.5 K |
|
|
331 | (11) |
|
7.6.1 Carbon-Based Adsorbers |
|
|
333 | (1) |
|
7.6.1.1 Activated Charcoal |
|
|
333 | (1) |
|
|
|
334 | (3) |
|
7.6.2 Amorphous Carbon Coating Absorption Properties |
|
|
337 | (1) |
|
7.6.3 Metal-Based Absorbers |
|
|
338 | (1) |
|
7.6.3.1 Aluminium-Based Absorbers |
|
|
338 | (2) |
|
7.6.3.2 Copper-Based Absorbers |
|
|
340 | (1) |
|
7.6.3.3 LASE for Providing Cryosorbing Surface |
|
|
341 | (1) |
|
7.6.4 Using Cryosorbers in a Beam Chamber |
|
|
341 | (1) |
|
7.7 Beam Screen with Distributed Cryosorber |
|
|
342 | (1) |
|
|
|
343 | (1) |
|
|
|
344 | (5) |
|
8 Beam-Induced Electron Multipacting, Electron Cloud, and Vacuum Design |
|
|
349 | (72) |
|
|
|
|
|
|
|
349 | (7) |
|
|
|
349 | (2) |
|
|
|
351 | (5) |
|
8.2 Mitigation Techniques and Their Impact on Vacuum Design |
|
|
356 | (9) |
|
|
|
357 | (6) |
|
|
|
363 | (2) |
|
8.2.3 What Techniques Suit the Best |
|
|
365 | (1) |
|
8.3 Secondary Electron Emission (Laboratory Studies) |
|
|
365 | (11) |
|
8.3.1 SEY Measurement Method |
|
|
365 | (2) |
|
8.3.2 SEY as a Function of the Incident Electron Energy |
|
|
367 | (1) |
|
8.3.3 Effect of Surface Treatments by Bakeout and Photon, Electron, and Ion Bombardment |
|
|
367 | (1) |
|
8.3.4 Effect of Surface Material |
|
|
368 | (1) |
|
8.3.5 Effect of Surface Roughness |
|
|
369 | (2) |
|
8.3.6 `True' Secondary Electrons, Re-Diffused Electrons, and Reflected Electrons |
|
|
371 | (3) |
|
8.3.7 Effect of Incidence Angle |
|
|
374 | (1) |
|
8.3.8 Insulating Materials |
|
|
374 | (2) |
|
8.4 How the BIEM and E-Cloud Affect Vacuum |
|
|
376 | (3) |
|
8.4.1 Estimation of Electron Energy and Incident Electron Flux |
|
|
376 | (2) |
|
8.4.2 Estimation of Initial ESD |
|
|
378 | (1) |
|
8.5 BIEM and E-Cloud Observation in Machines |
|
|
379 | (26) |
|
8.5.1 Measurements in Machines |
|
|
379 | (2) |
|
|
|
381 | (1) |
|
8.5.1.2 Vacuum Chamber Wall Properties |
|
|
382 | (4) |
|
8.5.1.3 Specific Tools for BIEM and Electron Cloud Observation |
|
|
386 | (4) |
|
8.5.2 Machines Operating at Cryogenic Temperature |
|
|
390 | (1) |
|
8.5.2.1 Surface Properties at Cryogenic Temperature |
|
|
391 | (3) |
|
8.5.2.2 Observations with Beams |
|
|
394 | (7) |
|
8.5.2.3 The CERN Large Hadron Collider Cryogenic Vacuum System |
|
|
401 | (4) |
|
8.6 Contribution of BIEM to Vacuum Stability |
|
|
405 | (2) |
|
8.7 Past, Present, and Future Machines |
|
|
407 | (2) |
|
|
|
409 | (1) |
|
|
|
409 | (12) |
|
9 Ion-Induced Pressure Instability |
|
|
421 | (50) |
|
|
|
|
|
|
|
421 | (1) |
|
|
|
422 | (25) |
|
|
|
422 | (3) |
|
9.2.2 Solutions for an Infinitely Long Vacuum Chamber |
|
|
425 | (1) |
|
9.2.2.1 Room Temperature Vacuum Chamber |
|
|
425 | (1) |
|
9.2.2.2 Cryogenic Vacuum Chamber |
|
|
426 | (1) |
|
9.2.2.3 Summary for an Infinitely Long Vacuum Chamber |
|
|
427 | (1) |
|
9.2.3 Short Vacuum Chamber |
|
|
428 | (1) |
|
9.2.3.1 Solution for a Short Vacuum Chamber with a Given Gas Density at the Ends |
|
|
428 | (3) |
|
9.2.3.2 Solution for a Short Vacuum Chamber with a Given Pumping Speed at the Ends |
|
|
431 | (3) |
|
9.2.3.3 Solution for a Short Vacuum Chamber Without a Beam Screen Between Two Chambers With a Beam Screen |
|
|
434 | (3) |
|
9.2.3.4 Some Remarks to Solutions for Short Tubes |
|
|
437 | (1) |
|
|
|
437 | (1) |
|
|
|
438 | (1) |
|
9.2.5.1 Solutions for an Infinitely Long Vacuum Chamber |
|
|
439 | (1) |
|
9.2.5.2 Solution for a Short Vacuum Chamber in the Equilibrium State |
|
|
439 | (1) |
|
9.2.6 Some Comments to the Analytical Solutions |
|
|
440 | (1) |
|
9.2.7 Effect of the Ion-Stimulated Desorption on the Gas Density |
|
|
441 | (1) |
|
9.2.7.1 Infinitely Long Vacuum Chamber (One Gas) |
|
|
441 | (1) |
|
9.2.7.2 Vacuum Chamber with a Given Pumping Speed at the Ends (One Gas) |
|
|
441 | (2) |
|
|
|
443 | (1) |
|
9.2.8 Some Numeric Examples from the LHC Design |
|
|
443 | (1) |
|
9.2.8.1 The Critical Current for an Infinitely Long Vacuum Chamber |
|
|
444 | (1) |
|
9.2.8.2 Short Vacuum Chambers |
|
|
445 | (1) |
|
9.2.8.3 Effect of the Ion-Stimulated Desorption on the Gas Density |
|
|
445 | (2) |
|
9.3 VASCO as Multi-Gas Code for Studying the Ion-Induced Pressure Instability |
|
|
447 | (8) |
|
9.3.1 Basic Equations and Assumptions |
|
|
447 | (1) |
|
9.3.2 Multi-Gas Model in Matrix Form and Fragmentation in Several Vacuum Chamber Elements |
|
|
448 | (1) |
|
9.3.2.1 Boundary Conditions |
|
|
449 | (1) |
|
9.3.3 Transformation of the Second-Order Differential Linear Equation into a System of First-Order Equations |
|
|
450 | (1) |
|
9.3.3.1 Boundary Conditions |
|
|
451 | (1) |
|
9.3.4 Set of Equations to be Solved |
|
|
451 | (1) |
|
9.3.5 `Single Gas Model' Against `Multi-Gas Model' |
|
|
452 | (3) |
|
9.4 Energy of Ions Hitting Vacuum Chamber |
|
|
455 | (9) |
|
9.4.1 Ion Energy in the Vacuum Chamber Without a Magnetic Field |
|
|
455 | (1) |
|
|
|
455 | (3) |
|
|
|
458 | (2) |
|
9.4.2 Ion Energy in a Vacuum Chamber with a Magnetic Field |
|
|
460 | (1) |
|
9.4.2.1 Vacuum Chamber in a Dipole Magnetic Field |
|
|
461 | (1) |
|
9.4.2.2 Vacuum Chamber in a Quadrupole Magnetic Field |
|
|
461 | (1) |
|
9.4.2.3 Vacuum Chamber in a Solenoid Magnetic Field |
|
|
462 | (2) |
|
9.5 Errors in Estimating the Critical Currents Ic |
|
|
464 | (3) |
|
9.5.1 Beam-Gas Ionisation |
|
|
465 | (1) |
|
|
|
465 | (1) |
|
9.5.3 Ion-Stimulated Desorption Yields |
|
|
465 | (1) |
|
|
|
466 | (1) |
|
9.5.5 Total Error in Critical Current |
|
|
466 | (1) |
|
|
|
467 | (1) |
|
|
|
467 | (4) |
|
10 Pressure Instabilities in Heavy Ion Accelerators |
|
|
471 | (44) |
|
|
|
|
|
471 | (1) |
|
10.2 Pressure Instabilities |
|
|
472 | (8) |
|
10.2.1 Model Calculations of the Dynamic Pressure and Beam Lifetime |
|
|
476 | (1) |
|
10.2.1.1 Closed System (Vessel) |
|
|
476 | (2) |
|
10.2.1.2 Vessel Including Collimation |
|
|
478 | (1) |
|
10.2.1.3 Longitudinal Profile |
|
|
478 | (1) |
|
|
|
479 | (1) |
|
10.3 Investigations on Heavy Ion-Induced Desorption |
|
|
480 | (25) |
|
10.3.1 Desorption Yield Measurements |
|
|
481 | (2) |
|
10.3.2 Materials Analysis |
|
|
483 | (2) |
|
10.3.3 Dedicated Set-ups to Measure Ion-Induced Desorption Yields |
|
|
485 | (4) |
|
|
|
489 | (1) |
|
|
|
490 | (3) |
|
10.3.4.2 Surface Coatings |
|
|
493 | (1) |
|
10.3.4.3 Cleaning Methods |
|
|
494 | (1) |
|
10.3.4.4 Energy Loss Scaling |
|
|
495 | (1) |
|
10.3.4.5 Angle Dependence |
|
|
496 | (1) |
|
|
|
497 | (1) |
|
10.3.4.7 Cryogenic Targets |
|
|
498 | (1) |
|
|
|
499 | (1) |
|
10.3.5.1 Interaction of Ions with Matter |
|
|
499 | (2) |
|
10.3.5.2 Inelastic Thermal Spike Model |
|
|
501 | (4) |
|
10.4 Conclusion: Mitigation of Dynamic Vacuum Instabilities |
|
|
505 | (2) |
|
|
|
507 | (1) |
|
|
|
507 | (8) |
| Index |
|
515 | |