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Secondary Electron Emission Data for the Simulation of Electron Cloud

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Secondary Electron Emission Data for the Simulation of Electron Cloud SECONDARY ELECTRON EMISSION DATA FOR THE SIMULATION OF ELECTRON CLOUD B. Henrist, N. Hilleret, M. Jimenez, C. Scheuerlein, M. Taborelli, G. Vorlaufer CERN, Geneva, Switzerland Abstract energy distribution. In such formulae, fitting parameters The secondary electron yield is one of the determinant must be determined by measurements of samples parameters entering in the simulation of the electron corresponding to the material investigated. This is cloud phenomenon. As secondary electron emission is a especially true in the case of accelerators as the surfaces surface process, it is strongly influenced by slight involved are far from being ideal but are technical modifications of the materials outer layers. This surfaces processed according to procedures applicable to presentation will try to summarize various numerical many square meters as this is the case for the copper formulae describing the main input data needed for the cladded LHC beam-screen. The following paragraphs will simulation of the electron multiplication in the electron give the fitting parameters that can be used to describe cloud process analytically the secondary electron emission of this surface. The copper samples were cleaned by immersion 1 INTRODUCTION in an alkaline detergent (NGL Cleaning Technology 17.40) followed by rinsing in demineralised water and The electron cloud effect [1-3] is a possible limitation ethanol. for the operation of LHC and of its injector, the SPS. Apart from dissipating an excessive power on the LHC 2.1 Variation of the S.E.Y. with the primary beam screen, it can induce detrimental oscillations of the electron energy proton beams which degrade their emittance and hence The secondary electron emission can be described using the achievable luminosity in the interaction points. a simplified two steps model [6, 7]: Accurate simulation programs are necessary to predict the - The deposition of energy by the primary electron at behaviour of future machines and adapt possible cures, a constant rate along its trajectory [8, 9] e.g. surface treatments, to meet the expected performance. - The escape of the created excited electrons with a The electron cloud mechanism depends partly on the probability decreasing exponentially with the generation of secondary electrons by electron impact on distance to the surface [10] the vacuum chamber hence it is important to provide, for The use of reduced S.E.Y. (ratio of the S.E.Y. to the the simulation programs good fits to analytical formulae maximum S.E.Y., δ ) and of reduced energy ( ratio of able to represent the main characteristics of the secondary m electron emission. This paper presents various equations from the existing literature and their comparison to data 1000 collected for the copper surface of the future LHC. 900 Ep= 10 eV 800 Ep=30 eV 2 EMPIRICAL FORMULAE AND 700 Ep= 100 eV NUMERICAL VALUES FOR 600 SIMULATIONS Ep=300 eV 500 Ep=550 eV For the simulation of the electron cloud phenomenon, it 400 is necessary to use various analytical formulae reproducing the variation of different characteristics of 300 the secondary electron emission. These formulae are also 200 very important in the field of surface physics e.g. for the 100 prediction of contrast in scanning electron microscopy[4], 0 or for the study of electronic devices using electron 0.00 0.20 0.40 0.60 0.80 1.00 mutiplication [5]. For this reason the mechanisms leading NORMALISED ENERGY to the secondary electron emission have been studied in details and appropriate analytical formulae either based Figure 1: Normalised secondary electron energy on physical models or purely empirical have been distribution for conditioned copper published. They describe the main features of the secondary electron emission, namely : the variation of the the energy to the energy of the maximum S.E.Y., Em) secondary electron yield (S.E.Y.) as a function of the allows to replace difficult to obtain constants by two primary electron energy (Ep) or the secondary electron more accessible quantities δm and Em. This useful normalisation [11] was used to give an analytical reflected peak and “intermediate”: electrons with an expression for the variation of the S.E.Y.[4, 7, 12] energy between 20 eV and the reflected peak energy . which was simplified by M. Furman [2, 12] to be Table 1: Fitting parameters for the expression of the incorporated in simulation codes of the electron cloud reflected fraction f in the case of copper effect. However this formula (1) : E Higher energy s× ( p ) Fitting Low energy coefficient (<300 eV) (1) δ = δ E MAX (<2000 eV) s MAX s E p A0 20.699890 0.300207076 s− 1+ E MAX A1 -7.07605 0.044915014 underestimates the S.E.Y. of primary electrons with very low energy [12]. This is due to the basic assumptions A2 0.483547 -0.155498672 quoted before which do not consider the possibility of A3 0 9.50318x10-4 reflection. This event has a high probability for low E0 56.914686 0 TRUE SECONDARIES < 20 eV FIT II low FRACT > 20 eV (reflected included) Curve label FIT II REFLECTED energy INTERMEDIATE ENERGY 90% To improve the accuracy of formula (1) for electrons of 80% low energy ( < 100 eV), measurements of the secondary 70% 60% electron energy distribution have been used to evaluate 50% the fraction (f) of reflected electrons in the total energy 40% distribution. Figure 3 shows this fraction in the case of FRACTION 30% 20% copper. To fit the experimental points (squares) the 10% expression described by Scholtz et al [13] has been used : 0% = + × + + × + 2 + × + 3 10 30 100 300 550 ln( f ) A0 A1 (ln(E p E 0 )) A2 (ln(E p E0)) A3 (ln(E p E0)) INCIDENT ELECTRON ENERGY (eV) where E p is the primary electron energy and the other Figure 2: Variation of the energy repartition of reemitted terms are fitting parameters given in table 1. electrons as a function of the primary electron energy (Ep) 2.2 energy incident electrons (E< 30 eV) as can be seen in 2.0 figure 1 which shows the normalised intensity ( 1 for the 1.8 highest peak) as a function of the normalised energy (1 CU AS RECEIVED for the incident energy). More generally, figure 2 gives 1.6 100% 1.4 1.2 EXPERIMENTAL DATA (AVERAGE ON 25 SAMPLES) 1.0 FIT FURMAN REF/TOT REFLECTED 0.8 FIT II FIT + REFLECTED 0.6 EXP FIT + REFLECTED FIT II LOW ENERGY SECONDARY ELECTRON YIELD ELECTRON SECONDARY 0.4 10% EXP FIT 0.2 0.0 0 200 400 600 800 1000 ENERGY (eV) RATIO REFLECTED/TOTAL REFLECTED/TOTAL RATIO Figure 4: Comparison between fitting formulae and 1% experimental data for as received copper. 0 100 200 300 400 500 600 The formula used to account for the reflected electron PRIMARY ELECTRON ENERGY contribution f at low energy combined with formula (1) Figure 3: The ratio (f) between the reflected and the total has been checked against the measured value of the total δ number of re-emitted electrons for copper (squares) and secondary electron yield ( t) in the case of as received the fitting laws copper. To calculate δt, the following formula was considered, whereδ is the true secondary yield given by the ratio between the various categories of reemitted S δ electrons for copper. These categories have been formula 1 and R is the yield of reflected electron: arbitrarily defined according to their energies (E) as “true δ =δ + δ secondaries”: (E < 20 eV), “reflected”: electrons: in the t S R , δ = ×δ ⇒ δ = δ + ×δ R f t t S f t this formula is only valid for true secondary electrons and 1 an upper limit is given in table 3 for the validity of this Hence: δ = δ × expression. This limit is usually around 20 eV but at very t s ()1 − f low primary energy it can be as low as 5 eV because of the importance of the reflected peak at this low incident A comparison of the fitting formula to experimental data energy and of the corresponding electron depletion at is given in figures 4 and 5 for the case of as received energies immediately lower. copper. Figure 5 is an enlargement of figure 4 for low incident energies. These fits were obtained using for the Table 3: Fitting parameters for various primary electron energies (formula 2) 1.8 PRIMARY CE0 τUPPER CU AS RECEIVED ENERGY ENERGY 1.6 (eV) BOUND 1.4 (eV) 10 0.277 1.57 0.985 5 1.2 30 0.136 1.9 0.99 22 1.0 100 .126 1.58 1.16 22 EXPERIMENTAL DATA (AVERAGE 300 .155 2.1 0.85 21 0.8 ON 25 SAMPLES) FIT FURMAN 550 0.2 1.48 0.909 26 0.6 REFLECTED FIT + REFLECTED SECONDARY ELECTRON YIELD ELECTRON SECONDARY 0.4 EXP FIT + REFLECTED 0.3 10 eV EXPERIMENT 0.2 0.25 FIT II 0.0 0.2 0 20406080100 ENERGY (eV) 0.15 Figure 5: Comparison between fitting formulae and 0.1 experimental data for as received copper at low incident 0.05 energy 0 formula 1 the parameters listed in table 2. The curves in 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 figure 5 show the importance of the reflected electron contribution to fit the low energy data with a good Figure 6: Comparison between the fitted curve and the accuracy. The increase of the secondary electron yield at experimental data for as received copper and 10 eV very low impact energy (below 5 eV) has been also primary electron energy measured for pure copper by Myers [14].
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