Ruthenium(II)-arene complexes with monodentate aminopyridine ligands: Insights into redox stability and electronic structures and biological activity

Accepted Manuscript Numerical study of the thermal performance of the CERN Linac3 ion source miniature oven C. Fichera, F. Carra, D. Küchler, V. Toivanen PII: DOI: Reference: S0168-9002(18)30641-7 https://doi.org/10.1016/j.nima.2018.05.036 NIMA 60820 To appear in: Nuclear Inst. and Methods in Physics Research, A Received date : 8 January 2018 Revised date : 26 March 2018 Accepted date : 15 May 2018 Please cite this article as: C. Fichera, F. Carra, D. Küchler, V. Toivanen, Numerical study of the thermal performance of the CERN Linac3 ion source miniature oven, Nuclear Inst. and Methods in Physics Research, A (2018), https://doi.org/10.1016/j.nima.2018.05.036 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. 1 2 Numerical study of the thermal performance of the CERN Linac3 ion source miniature oven 3 C. Fichera1, F. Carra1, D. Küchler1, V. Toivanen2 4 1 European Organization for Nuclear Research (CERN), Geneva, Switzerland 5 2 Grand Accélérateur National d’Ions Lourds (GANIL), Caen Cedex, France 6 7 8 9 Abstract 10 11 12 13 14 15 16 17 18 19 20 21 22 23 The Linac3 ion source at CERN produces lead ion beams by the vaporization of solid samples inside the internal ovens and the consequent ionization of the evaporated material in the plasma. The geometry, materials and surface state of the oven elements are critical parameters influencing the oven temperature characteristics and consequently the evaporation properties and the ion source performance. A dedicated test stand was assembled and a finite element approach is proposed to evaluate the thermal response of the system at increasing heating powers. Comparisons between the simulation results and experimental measurements are given in order to validate the numerical model. Radiation was found to be the main heat transfer mechanism governing the system. Based on the obtained results, improvements to the existing setup are analysed. 24 1. Introduction 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 In the framework of the High Luminosity project of the Large Hadron Collider (HL-LHC), all the LHC injectors are undergoing an extensive upgrade program, named LHC Injector Upgrade (LIU) [1]. The first link of the heavy ion accelerator chain is represented by the Linac3 linear accelerator, Fig. 1, operating since 1994 [2]. As a part of the Linac3 upgrades, several activities involve the GTS-LHC Electron Cyclotron Resonance ion source (ECR), which produces the primary heavy ion beams [3]. The major efforts focus on the GTS-LHC extraction region, the double frequency plasma heating combined with afterglow operation [4] and the oven studies for metal ion beam production [5]. Concerning the oven studies, the lead ion beams delivered by the Linac3 are produced with the ECRIS using resistively-heated miniature ovens. Since the oven performance is related to the temperature distribution, a dedicated off-line test stand was built with the capability of measuring the oven temperatures and a numerical thermal model was developed to complement the measurements and evaluate the criticality of the several parameters involved. The application of the finite element method in the study of an ion source is a novelty in the accelerator community. In the following chapters the features of the advanced numerical method developed using the ANSYS Workbench finite element code [6] are described in detail, focusing the attention on the loading conditions, the material data and the assumptions adopted. The theoretical principles of the heat exchange are recalled to justify the assumptions taken. A benchmarking is performed between the numerical results and the experimental data in order to validate the numerical model. Finally, some recommendations are given for future and similar Keywords: Linear accelerator; accelerator equipment design; CERN; finite elements method; numerical thermal analysis; heat transfer. 45 46 technoloogies and new n solution ns are prop osed to imp prove the performancee and servicce life of the sourrce. 47 48 Figurre 1 The CERN accelerator com mplex 49 2. Co omponen nt descr ription 50 51 52 53 54 55 56 57 58 59 60 61 Thhe GTS-LH HC 14.5 GH Hz ECR ionn source, Fig. F 2, proviides highly--charged heeavy ion beams, predominanntly lead, for f the CER RN experim ments. The beam is geenerated fro om solid materiall evaporatedd in the ion source plassma chambeer with resisstively-heatted ovens. The T oven consistss of a long vacuum--sealed staiinless steell cane1, wh hich contaiins a copp per wire connectted, at the end e of the cane, c to a taantalum heaating filameent wound aaround the crucible. c The canne allows thhe axial inseertion of thhe oven thro ough the ion n source injjection plug g, Fig. 3. The cruucible is maade of alum mina, as welll as the fillament supp port and inssulator. Fin nally, the cruciblee is positionned inside a tantalum shhell which is i connected d to the canne, Fig. 4. The T outer diameteer of the oveen is 14 mm m and the tootal length, including the t cane, is 870 mm, while w the diameteer of the taantalum filaament is 0..45 mm. Att the tip off the oven,, two holess with a diameteer of 1.5 mm m and 5.5 mm m in the cruucible and the t tantalum m cover, resp spectively, allow a the evaporaation of neuttral atomic lead. The syystem can be b dismountted to refill the cruciblee. 1 This de esignation is technically used u to identtify the cylin ndrical shell containing c th he current lea ad. -2- 62 63 64 Figure 2 Linac3 GTS-LHC C ECR Ion Source (forr clarity, the extractionn vacuum pumps p are not shoown). 65 66 Figuree 3 Crosss section off the Linac3 GTS-LHC ECR Ion SSource. -3- 67 68 Figure 4 GTS-LHC C resistively y-heated min niature ovenn. 69 70 71 72 73 74 Thhe crucible refilling iss required every 2-3 operating weeks w due to degradin ng beam perform mance. In soome instances, the beam m productio on is interru upted by bllockage of the t oven tip, eithher by formation of leaad oxide or droplets off metallic leead [5]. Thhese issues could c be provokeed by non-hhomogeneo ous temperaature distrib bution alon ng the cruciible or tem mperature gradientts in the neuutral lead ex xit zone. In that sense, the thermal analysis oof the system m should provide further detaails about th he oven behhaviour. 75 3. Exp perimen ntal mea asureme ents 76 77 78 79 80 81 82 83 84 85 86 87 88 A dedicated off-line test stand wass built at CE ERN for monitoring m thhe behaviou ur of the oven duuring the heeating proceess, acquirinng the most relevant physical p quaantities, succh as the temperaature in fixeed points and a the leadd evaporation rates [5]. In particcular, the oven was equippeed with vaccuum-grade thermocouuples in ord der to measure the innternal and external temperaature. The thermocoup t le measurinng the temp perature inside the oveen was secu ured to a copper pin 23 mm m long with h a diameteer of 3 mm m. The copp per pin is inserted in nside the aluminaa crucible and a replacess the lead inn order to perform p measurementss up to 1000 0 °C. On top of tthat, an addditional therrmocouple was attacheed to the outside surfaace of the tantalum t shell, pllaced at thee axial locattion correspponding to the t centre of o the crucibble. In this case, c the thermoccouple was fixed with a clampingg system made m of a staainless steeel ring and a central screw, aas shown inn Fig. 5. In normal n operration, the oven o heatin ng power is limited to 20 2 W. In Fig. 6, tthe experim mental temp peratures aare reported d as a funcction of thee heating power p in steady-sstate conditiions. -4- 89 90 91 Figure 5 left) Sttainless steeel holder rinng for therrmocouple installation i and right) setup for oven teemperature measuremen m nts. 93 94 Figure 6 Measurred temperaature vs. ovven power:: crucible (red ( solid lline) and oven o body temperaature (blue solid line). 95 96 97 98 Foor the prodduction of lead l beamss, the oven is normally operated with poweer levels above 6 W. One can observe that thee measured d oven tem mperatures follow a T ∝ P1/4 relationship, wheree P is the power p to thee oven. Usu ually, this behaviour b iss typical off thermal radiationn problems, as will be shown in thhe following g section. 99 4. He eat transfer me echanism ms 100 101 102 103 104 105 Thhe heat traansfer mech hanisms govverning thee system un nder study were exam mined in detail too determinee the most appropriate a material paarameters an nd boundaryy condition ns for the thermal analysis. The T conserv vation of ennergy specifies that neet exchangee of the eneergy of a system is always equal e to thee net transfeer of energy y across thee boundary system as heat h and work; aapplying thiis to a diffferential voolume and considering c g the time vvariable t, the heat equationn assumes the t followin ng differentiial form: 106 (1) 92 -5- 107 108 109 Thhe first term m representts the transsient part in n which thee energy is released or stored, where cp is the speecific heat capacity andd ρ is the deensity. The second term m is the tem mperature variationn along the componeent, where k is the th hermal conductivity an and the Laplace 110 operatorr, 111 112 113 114 115 116 rate perr unit volum me. The material m propperties are a function of the tem mperature. The T heat equationn is a partiaal differentiaal equation that describ bes the distrribution of hheat (or varriation of temperaature) in a given g region n over timee. In some cases, exact solutions of the equaation are availablle; in otherr cases thee equation must be solved s num merically ussing compu utational methodss. In a steaady-state caase, the therrmal gradieent is constant with tim me, 0 and the equationn (1) simpliifies to: 117 (2) 118 119 Inn this work it is assum med that, booth in the measuremen m nts and in tthe simulatiions, the steady-sstate conditiion is reach hed and (2) aapplies. 120 121 Thhe exchangge of energ gy in the system is regulated by the com mbination of three fundamental modess of heat traansfer: condduction, con nvection and d radiation. 122 4.1 Co onduction n 123 124 125 126 Inn the heat exxchange by conductionn, the internal heat transsfer occurs between tw wo points of the saame body or o two bodiees in contacct. The temp perature graadient on a bbody in steaady-state conditioons follows the definitiion in (2). IIn the case of o two bodiies in contacct, such as A and B in Fig. 77, the therm mal flux betw ween two pooints is: 127 ∆ in n Cartesian coordinates, while Q is the interrnal heat geeneration (3) ∆ ∙ ∙ ∙ 128 129 Figure 7 Thermal fflux betweeen two solid ds in contactt. 130 131 132 133 134 135 136 137 138 whhere S is thhe contact arrea, x the oorthogonal direction, d ΔxxA and ΔxB the distancees of the measuriing points 1 and 2 from m the interfface. The th hermal flux thus depennds on the geometry g of the bbodies, on thheir thermal conductivvity and on the t coefficient hc, whicch is called d thermal contact conductancce. This parameter is off paramoun nt importancce in the casse of heat exchange e betweenn two good conductorss, where moost of the temperature t gradient iss often geneerated at the inteerface. The contact con nductance iis influenceed by many y factors, thhe contact pressure being thhe most im mportant. The T influencce of the contact c preessure on th the thermall contact conducttance has been b widely y discussedd by many y authors [7,8] and thheir relatio onship is typicallyy expressedd as follows: 139 1.25 140 141 whhere ks is thhe harmonic mean of tthe thermall conductiviities, σ is thhe roughnesss and m the relaated surface slope, while w P is the contacct pressure and He thhe effectivee elastic -6- . (4) 142 143 144 145 micro-hardness. Considering the system under study, most of the bodies in contact have a very low contact pressure, comparable to that generated by their deadweight, and the contribution of thermal conduction in the heat exchange between bodies in contact is expected to be negligible with respect to the heat exchanged by radiation (see section 6.3). 146 4.2 Convection 147 148 149 Convection is the thermal exchange between a body and a surrounding fluid in motion. The basic relationship for the convection heat transfer is defined by the Newton’s law of cooling: 150 (5) 151 152 153 154 155 156 157 where q is the heat flow between the body surface and the fluid, A the body surface in contact with the fluid, h the thermal convection coefficient and Ts and Tf are the absolute body surface and fluid temperatures, respectively. On the basis of the fluid motion, the convection may be classified as free (or natural) or forced. In the forced case, an artificially-induced convection current is created when a fluid is forced to flow around the body surface by means of an external source, such as a pump. In the case of natural convection, an increase of the temperature produces a reduction in the fluid density, which in turn causes the fluid motion. 158 159 In the system under study, the oven operates in vacuum and the convection contribution to the heat transfer is negligible. 160 4.3 Radiation 161 162 163 164 165 166 The thermal energy between two bodies is also exchanged through electromagnetic radiation. This mechanism is known as thermal radiation, because the random movement of atoms and molecules in a body, composed of charged particles, results in the emission of electromagnetic waves, which carry energy away from the body surface. Unlike convection, thermal radiation occurs also under vacuum. The transfer of radiant energy is described by the Stefan-Boltzmann’s equation, which for two grey-body surfaces can be written as follows: ∙ 167 ∙ 168 → ∙ where: 169 Q is the heat flux; 170 σ is the Stefan-Boltzmann constant; 171 (6) ∙ , are the emissivities of the surfaces 1 and 2 (equal to 1 for a black body); 172 A1,2 are the surface areas 1 and 2; 173 F1→2 is the shape factor; 174 T1,2 are the absolute temperatures in Kelvin of surfaces 1 and 2. 175 176 177 178 179 In (6), only the emissivity depends on the material, while the other parameters are constant or depend on the geometry. The emissivity represents the material effectiveness in emitting thermal radiation and is generally measured as the ratio of the thermal radiation from a surface to the radiation from an ideal black body surface at the same temperature. The ratio varies from 0 to 1. Kirchhoff’s law equates the emissivity of an opaque surface with its -7- 180 181 182 183 184 185 186 187 absorption of incident radiation. The largest absorptivity corresponds to complete absorption of all incident light by a truly black object, explaining why mirror-like and polished metallic surfaces that reflect light will thus have low emissivity. For several applications, when conduction and convection are present, radiation becomes relevant only at high temperatures. In the case under examination, radiation actually is the most relevant mechanism of heat exchange also at low temperatures, given the absence of the convection contribution and the low contact pressure between most of the components in contact, which minimizes the thermal exchange by conduction (see section 6.3). 188 5. Materials 189 190 191 192 193 194 195 196 197 198 199 200 201 As seen in section 4, the heat flow and the temperature gradient in steady-state conditions of the problem under study depend on the thermal conductivity and the emissivity of the materials. These properties are temperature-dependent, and available in literature for all the materials adopted in the analysis [9-11]. The emissivity, on the other hand, is strictly related to the surface state of the radiating bodies [10]. Fig. 8 shows the emissivity values for alumina, copper, stainless steel and tantalum as a function of temperature and surface state. It is important to underline that in the numerical analysis the data is linearly extrapolated for the higher temperatures. It is evident that, in general, the surface state consistently influences the emissivity. Nevertheless, the surface state can be challenging to assess accurately considering that it usually changes with time. The metal parts of the oven are machined without applying a finishing polishing and are then operated at high temperatures in a residual gas atmosphere with always some low level oxygen residue. Therefore, the surface conditions of the materials are expected to be between the polished and oxidized limits. -8- 202 203 204 205 206 Figure 8 207 6. Nu umerical model 208 6.1 Bo oundary conditions c s 209 210 211 212 213 214 215 216 217 218 219 220 Given the complex natu ure and nonllinearities of o the probleem, a finitee-elements approach a was adoopted to model the systtem and the calculation n was perforrmed with A ANSYS Wo orkbench 17.2. Inn the simulaation, the oven o geomeetry was rep produced with w a 2D-ax axisymmetriic model and thee cane lenggth reduced d to 250 m mm, which is the leng gth containned in the vacuum enclosurre of the offf-line test stand. Room m temperatu ure was imposed at the end of the stainless steel canne, as meassured at the vacuum seaal during ov ven heating. In additionn, an extern nal frame was creeated at 10 mm m radial distance d froom the oven n which dirrectly exchaanges heat with the surrounding ambieent at the co onstant tempperature of 22 °C, Fig. 9. It is imp mportant to highlight h that thee vacuum enclosure e of o the off-liine test staand is roug ghly 50 mm m around th he oven; nevertheeless, althoough the ex xternal fram me in the model is much m closeer to the oven, the numericcal results did not show significcant differeence movin ng it from 50 to 10 mm. m The distancee was set at 10 mm resu ulting in deccreased calcculation tim mes. Emissivvity vs. tem mperature ass a function n of the surrface state ffor: top left) ft) alumina (Al2O3), ) top right)) copper, bbottom left) stainless stteel and boottom right)) tantalum [10,11]]. -9- 221 222 223 224 225 226 227 228 229 230 231 Figure 9 2D-axissymmetric model m and materials. m Thhe heat trannsfer betweeen the compponents was modelled imposing a perfect surface-tosurface radiation, i.e. the total amount off energy excchanged insiide a defineed enclosuree. In this case, thhe perfect enclosure e iss the wholle area insiide the sim mplified exteernal framee, where surface--to-surface radiation occcurs betweeen the maiin system elements. Inn such enclo osure the net totaal radiationn is zero. The T emissivvity was im mposed to the materiaals as a no on-linear functionn of the tem mperature, according to the dataa from literature (Figg. 8). The boundary b conditioons are sum mmarized in Fig. 10. Fiinally, the convection c contribution c n was negleected for the reassons mentiooned in secttion 4, whille the condu uction throu ugh the therrmal interfaaces was estimateed according to (3) (seee section 6.33). 232 233 Figuree 10 Bounddary condittions of the model. 234 6.2 Mesh 235 236 237 238 239 240 241 242 243 244 Thhe model feeatures abou ut 7000 plaane elementts and the minimum m eddge length is i 35 µm for elem ments in the filament reegion. For m meshing, thee PLANE77 7 element off ANSYS was w used, which iss an 8-nodee thermal element withh one degreee of freedom m at each noode. Moreo over, this elementt is well suiited to mod del curved bboundaries because qu uad/triangullar-shaped elements e may be formed. Thhe mesh quaality assessm ment was peerformed in nvestigating the elemen nt quality functionn, which proovides a com mposite quaality metricc that rangess between 0 and 1. Thiis metric is basedd on the raatio of the volume to the sum of the squarre of the eddge lengthss for 2D elementts. A value of o 1 indicates a perfectt square while 0 indicattes that the element has zero or negativee volume. In I the preseent model, the elemen nt quality iss over 0.9 ffor more th han 6500 elementts, i.e. 93% of the total.. 245 6.3 Co ontacts 246 247 248 249 250 251 252 253 Foor most of the t compon nents in conntact inside the oven, the pressuree at the inteerfaces is very low w and the body-to-body conducttive heat traansfer can be consideered negligible with respect to the radiaative one. Indeed, I as sshown in (4 4), for a low w contact ppressure thee thermal conducttance coeffficient, hc, approachees zero and, consequ uently, accoording to (3), the conducttive heat floow approach hes zero. T The contact pressures were w calculaated consideering the deadweight of the components c s. Neverthelless, in all cases, c the th hermal condductance co oefficient is almosst negligiblee (less than 0.1 Wm-2K -1), except for the oveen-to-cane bbolted conneection in stainlesss steel (see Fig. 11), for f which a thermal co onductance coefficientt of 14500 Wm W -2K-1 - 10 - 254 255 was callculated asssuming a tightening toorque of 2 Nm, N which correspondds to 1 kN of axial force, between the two components with M M12 thread d. 256 257 Figu ure 11 Ov en-to-cane bonded b con ntact. 258 6.4 Th hermal loads 259 260 261 Inn normal operation the oven heatinng power is limited to 20 2 W and, bbased on the resistive power llosses, one can estimaate the pow wer distributtion in the different coonductors (Tantalum ( (Ta), Coopper (Cu) and a stainlesss steel (SS))) as follows: 7 262 263 where: ∙ 264 265 266 267 268 ∙ 8 ∙ Pi is either PTa, PCu or PSS, while I is the curreent flowing through thhe conductors, as it is the sam me through all a of them and thus ddisappears from f the eq quation, the power ratiios can be calculatted. The connductors in n the oven aare: the tan ntalum filam ment, the coopper wire inside the cane andd the stainleess steel can ne which accts as a returrn conducto or for currennt circuit. 269 Cond ductor Ta filament Cu wire SS cane Length l (mm) 700 760 760 Table 1 : Power disstribution raatios. Reesistivity φ Cro oss section A (mm2) (nΩ·m) 131 0.159 16.78 0.785 690 40.84 Po ower ra atio 0..952 0..027 0..021 270 271 272 273 274 275 276 277 Thhe rough esstimation of o the poweer distributiion reported d in Table 1 does not take into accountt the resistivvity depend dence with tthe temperaature, but co onsiders connstant valuees at room temperaature. On thhe other han nd, most off the contriibution to the t total poower comess from the tantalum m filament, which resu ults to it beeing the mo ost heated and a affectedd by the tem mperature increasee. Taking into i accoun nt that thee resistivity y usually increases ass a functio on of the temperaature, the reelative con ntribution off tantalum to the totaal power w would slighttly further increasee, approachiing a value of 1. The eerror in the assumption n of constant nt electrical resistivity with tem mperature iss therefore less l than 5% %. 278 279 280 281 Coonsidering the t power distribution d p is app pplied in thee model as ratios in Taable 1, the power an interrnal heat generation g (IHG) ( to eaach compon nent. Six different d theermal analy yses were perform med, with power p vary ying from 1 to 20 W; W the poweer has been en distributeed in the conducttors as reporrted in Tablle 2. - 11 - 282 Cond ductor Ta fiilament Cuu wire SS cane Taable 2: Pow wer distributiion in the co onductors. Total pow wer (W) Volume 1 2.5 5 10 15 (mm3) Distributed D power (W)) 112.4 0.952 2.380 4.760 9.520 14.280 270.1 0.021 0.053 0.106 0.212 0.318 11728.4 0.027 0.067 0.134 0.268 0.402 20 19.040 0.424 0.536 283 6.5 So olution algorithm 284 285 286 287 288 289 290 291 292 293 294 295 296 It is of interest to detail the numericcal method adopted by the finite eelement cod de to solve the therrmal probleem. As desscribed aboove, the thermal radiaation is thee main heaat transfer mechannism betweeen differentt bodies. R Radiation an nalyses are highly nonnlinear, with h the flux varying with the fourth f poweer of the boody’s absollute temperaature, as seeen in Eq. 6, 6 and the iterativee solution iss based on a convergennce criterion n. The radio osity solver m method is well w suited for genneralized raddiation pro oblems in 22D/3D invo olving two or more raadiating su urfaces. In ANSYS S, this methhod can be used for eeither transient or steaady-state thhermal anallyses. The radiosityy solver meethod is bassed on the hheat exchan nge between n radiating bbodies by solving for the outggoing radiattive flux forr each surfaace, when th he surface temperature t es for all su urfaces are known. Considerinng two radiaating surfacces i and j, Fig. F 12, the energy leavving the un nit area dA in all diirections is B, thereforre the total energy leav ving the surrface i ( ∙ ) can be b divided into its own radiannt componeent and the diffuse refflection of the t radiancee coming from fr other surfacess. 297 298 Figure 12 2 Heat excchange betw ween radiatin ng bodies. 299 300 301 302 Thhe total radiiant energy correspondds to (6), sim mplifying th he emission density Ei multiplied m by the uunit area ( ∙ ). Th he diffuse reeflection is the multipliication of thhe diffuse coefficient c Φi and tthe part of energy com ming from oother surfacces which reeaches the surface i. In ntegrating the conttribution of all surfacess, the formuula of the rad diosity of th he surface i is the follow wing: 303 304 305 306 307 308 309 ∙ ∙ ∙ ∙ ∙ (9) W Where Fij is the shape factor whicch determin nes the fraction of totaal energy leeaving the surface j which reaches the surface s i. Thhe surface fluxes prov vide boundaary conditio ons to the finite ellement moddel for the conduction c process anaalysis. The heat conduuction is gov verned by Fourier’’s law (1) and a for stead dy state prooblems the solution s onlly requires tthe knowled dge of the thermal conductiviity (2). When new surrface tempeeratures are computed, due to eith her a new step or iteration cyycle, new surface s fluxx conditionss are found d by repeatiing the pro ocess. The - 12 - 310 311 surface temperatures used in the computation must be uniform over each element surface facet to satisfy the conditions of the radiation model. 312 7. Results 313 314 315 316 317 318 319 In order to benchmark the experimental data, different simulations were run at increasing heating powers. While the thermal conductivity of the components as a function of temperature is well known from literature, the emissivity is the main variable affecting the thermal distribution. The range of values for the emissivity of each component was narrowed through bibliographic research, however, the emissivity strongly depends on the material surface state, which is unknown a priori. Parametric simulations were thus performed as a function of the different emissivities, to investigate the thermal response of the system. 320 7.1 Case 1 321 322 In the first case study (Case 1), the surface state was considered polished and cleaned for all the components. The emissivities used, extracted from Fig. 8, are reported in Table 3. 323 324 325 In Fig. 13, the temperatures obtained experimentally and numerically at the probe positions are compared. It is possible to observe that the numerical results overestimate the temperature distribution inside and outside the oven. 326 Alumina T (°C) -167 121 260 538 815 1093 1371 Table 3: Material emissivities for Case 1 [10,11]. Tantalum Stainless Steel Copper T (°C) 0.700 0.750 0.700 0.600 0.500 0.400 0.380 -212 149 204 427 593 871 1204 T (°C) 0.020 0.030 0.035 0.050 0.060 0.075 0.090 -18 65 154 204 260 316 427 327 - 13 - T (°C) 0.140 0.150 0.160 0.170 0.180 0.190 0.210 25 120 260 330 400 470 540 0.040 0.045 0.060 0.075 0.100 0.140 0.180 328 329 Fiigure 13 Numerical-e N experimentaal compariso on for Casee 1. 330 7.2 Ca ase 2 331 332 333 As opposed to t Case 1, Case C 2 assuumes heavilly oxidized surfaces. T The numericcal results are mucch closer to the experim mental meassures, Fig. 14. 1 The emiissivities addopted are reeported in Table 4. 334 335 Fiigure 14 Numerical-e N experimentaal compariso on for Casee 2. 336 - 14 - 337 Table 4: Material emissivities for Case 2 [10,11]. Tantalum Stainless Steel Copper Alumina T (°C) -167 121 260 538 815 1093 1371 T (°C) 0.700 0.750 0.700 0.600 0.500 0.400 0.380 -212 93 871 T (°C) 0.185 0.410 0.420 -18 65 154 204 260 316 427 T (°C) 0.850 0.820 0.825 0.835 0.850 0.860 0.875 315 400 470 540 610 675 745 0.475 0.500 0.540 0.575 0.625 0.700 0.800 338 339 340 341 342 343 344 The real scenario lays between the two extremes, Case 1 and Case 2. In fact, even if the initial surface state of the components is measurable, the level of oxidation changes with time and heating cycles. Several simulations were performed with different emissivity values for the materials, depending on the different oxidation levels assumed. Sensitivity analyses showed that the results were mostly sensitive to the variation of the emissivity of tantalum. Out of the tens of different combinations simulated, two additional cases to Case 1 and Case 2 are reported in this work. 345 7.3 Case 3 and 4 346 347 348 349 350 351 352 353 354 Section 7.2, and in particular Case 2, shows that the assumption of oxidized materials well represents the behaviour of the oven in operation. While the exact grade of oxidation of the components is uncertain, one can deduce, looking at Fig. 14, that it is lower than what assumed in Case 2. A fine-tuning of Case 2 was therefore performed in terms of emissivity of the tantalum, which resulted, out of the sensitivity study performed, the most influent parameter in the determination of the results. Two additional cases, with intermediate tantalum oxidation, Case 3 and Case 4, were run. For the new cases, a simple linear relationship between emissivity and temperature was assumed. The tantalum emissivities used in the four cases are reported in Table 5 and, for the sake of clarity, their difference is graphically shown in Fig. 15. 355 Case 1 T (°C) -212 149 204 427 593 871 1204 Table 5: Tantalum emissivities for different cases simulated. Case 2 Case 3 Case 4 T (°C) 0.020 0.030 0.035 0.050 0.060 0.075 0.090 -212 93 871 T (°C) 0.185 0.410 0.420 -212 1204 356 - 15 - T (°C) 0.080 0.200 -212 1204 0.150 0.300 357 358 Figgure 15 Em missivity vss. temperatuure for tantaalum in the different caases simulatted. 359 360 361 362 363 Thhe results with w the neew ranges of the tanttalum emisssivity are sshown in Fig. F 16. In additionn, the root-m mean-squaree error (RM MSE) for eaach case is reported r in order to esttimate the differennces betweeen the simu ulated resultts and the experimenttal measurees. Case 4 shows s the best agrreement witth the experrimental datta. This sceenario features an interrmediate ox xidation of tantalum m which is also a compattible with thhe visual insspections peerformed onn the compo onent. - 16 - 364 365 Figuure 16 Num merical-expperimental comparison for cases 1 to 4. - 17 - 366 367 368 369 370 Figure 117 Case 4 model: sim mulated tem mperature distribution d inside the GTS-LHC miniature oven with w 15 and 20 W heatinng powers. The oven tip t is at the top. Tempeeratures at locationns 1, 2 and 3 are 482, 834 and 870 °C for th he 15 W caase and 536 6, 915 and 960 °C for the 20 W case. 371 372 373 374 375 376 377 378 379 380 Fiig. 17 preseents the calcculated tempperature disstributions inside i the ooven with 15 W and 20 W heating pow wers. It is po ossible to oobserve thatt a rather good g temperrature unifo ormity is achieved along thee crucible, while w the tipp of the ov ven remains significanttly colder. At A 20 W the tem mperature grradient betw ween the m material in th he crucible (point 3) aand the cru ucible tip (point 22) is about 45 4 °C, while between tthe cruciblee tip and the oven tip ((point 1) it is about 420 °C. This relevvant gradien nt between the inner and a outer paart of the ooven can bee further highlighhted observving the heaat flux in Fiig. 18. Indeed, the heat flux is cooncentrated between the filam ment, i.e. thhe heating source, and the cruciblee confining most of thee energy aro ound the copper ppin. - 18 - 381 382 Figurre 18 Casee 4 model: hheat flux (W Wm-2) at 20 W heating power. 383 8. Sy ystem op ptimizattion 384 385 386 387 388 389 390 391 392 Thhe tantalum m emissivity y was foundd to be the most impo ortant param meter influeencing the behavioour of the system. s Neevertheless, the emissiivity depen nds on the surface staate, which changess during tim me due to ox xidation. Thhis effect caan be taken into considderation intrroducing a relationship betweeen time and d emissivityy for tantalu um. In orderr to do so, tthe emissivity should be meassured at diffferent work king times iin the test bench b oven, predicting the behaviour of the componnent during operation in the ion soource. Of course, this method is eeffective if the initial emissivity and surface state of o the tantaalum used in the test bench b and iin the sourcce are the same. IIn that sensse, surface treatments,, such as sandblasting s g or ion boombardmen nt, can be effectively perform med to impose the desirred surface state s to the component c [12]. 393 394 395 396 397 398 399 400 401 402 403 M Moreover, thhe calculateed temperatture distribu ution insidee the oven shows a good g axial uniform mity at diffeerent heating g powers; nneverthelesss, the tempeerature dropp in the oven tip has given thhe first hintss to possiblee causes of the observeed early red duction of thhe oven performance. Indeed, in normal operation o th he two ovenns installed in i the GTS--LHC proviide 2-3 weeeks of lead beam opperation bettween refillls. Howeverr, it was ob bserved that when a reffill is requirred due to degradinng beam peerformance,, typically aabout 2/3 of o the lead is i still left iin the oven n. In some cases thhe operationn is also interrupted byy blockage of o the oven tip, either by formatio on of lead oxide orr droplets of o metallic lead l which could be caused by th he cold ovenn tip observ ved in the simulatiions. In ordder to reducce the tempperature graadient in th he oven tipp, a possiblee solution could bbe to improove the filaament windding around d the crucib ble, exploititing all the available space, iin particularr close to th he tip. Addditionally, in ncreasing th he contact ppressure between the - 19 - 404 405 componnents wouldd enhance th he heat trannsfer by conduction, facilitating f tthe thermal diffusion and reduucing the teemperature gradients g beetween the oven o parts. 406 407 408 409 410 411 412 The effeectiveness of o these two o last propoosals was an nalysed by means m of nuumerical sim mulations. Concernning the fillament win nding, the ooven geomeetry was modified m exttending thee filament support in order too exploit all the free sppace close to o the oven tip (Fig. 199 centre). In nstead, the enhanceement of thhe thermal diffusion d byy conductio on was sim mulated settiing a perfect contact betweenn the tantaluum reflecto or foil and th the oven cover. In Fig.. 19 the tem mperature diistribution obtainedd at 10 W in these tw wo cases iss compared d with whatt obtained w with the baaseline of Case 4. 413 414 415 416 417 Figure 119 Temperrature distriibution of ddifferent nu umerical sim mulations aat 10 W oveen power: left) acctual oven n geometryy radiation dominated d, centre) modified geometry exploitiing the avaiilable spacee close to th he oven tip and right) aactual oven geometry with the tantalum reflector r foiil in contactt with the ov ven cover. 418 419 420 421 422 423 424 425 426 427 428 Thhe comparisson shows that t the exteension of th he filament support s up tto the tantallum cover slightly modifies itts temperatu ure distributtion with resspect the original ovenn geometry. However, this soluution has noo relevant effect e on tem mperature along a the crrucible and,, in particullar, on the temperaature gradiennt in the ov ven tip, whicch is about 315 °C as in n the baselin ine case. On n the other between th side, ennhancing thhe thermal conduction c he reflectorr foil and thhe oven co over has a relevantt influence on o the therm mal behavioour of the sy ystem. Indeeed, the firstt evident reesult is the drop-off ff, by aboutt 60 °C, of the temperrature in thee inner sidee of the ovven; neverth heless, the temperaature uniforrmity is maaintained allong the crrucible. Thiis effect is complemen nted by a temperaature increasse of about 30 °C in thhe tantalum cover due to t the therm mal diffusion n between the refleector foil annd the coveer. The tempperature graadient in thee oven tip iis reduced to t 230 °C, 30% lesss than the gradient g of the t baselinee case. - 20 - 429 9. Conclusions 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 An advanced numerical study was performed with the finite-elements method to evaluate the temperature distribution in the miniature ovens installed in the Linac3 GTS-LHC ECR ion source and assess the thermal behaviour of the system, which strongly influences the operational performance of the component. The thermal radiation was determined to be the main contribution to the heat exchange between the oven parts. The numerical model was benchmarked with measurements taken in an offline test stand which reproduces the same environment and thermal system of the ion source. The numerical simulations provided good agreement with the experimental data and, analysing the results, the tantalum emissivity turned out to be the crucial parameter influencing the behaviour of the system. Since the emissivity depends on the surface state, a satisfactory numerical-experimental benchmarking was obtained assuming intermediate conditions in terms of tantalum oxidation. Proposals to improve the thermal performance of the system were discussed considering the experimental observations and numerical outcome. Numerical simulations shown that introducing the thermal conduction between bodies allows to improve the temperature distribution of the system and, consequently, the service life of the source. Finally, the results obtained allowed to pinpoint general guidelines which could be beneficial also for similar systems and technologies. First of all, it is fundamental to assess and control the surface state of the components at the beginning of their life, and evaluate the evolution of the oxidation of the equipment during operation. Moreover, the emissivity of the adopted materials has to be carefully measured as a function of the surface state and oxidation on material samples. Finally, in order to obtain a more accurate model validation and monitor the temperature gradients along the structure components, the data acquisition system in dedicated test benches should feature an increased number of measuring points. 453 References 454 455 [1] G. Apollinari et al., “High-Luminosity Large Hardon Collider (HL-LHC): Preliminary Design Report”, Rep. CERN, CERN-2015-005, 2015. 456 [2] 457 458 459 [3] L. Dumas et al., “Operation of the GTS-LHC Source for the Hadron Injector at CERN”, in Proc. of ECRIS 2006, Lanzhou, China, published in HEP & NP, Vol.31, Suppl.1, pp.51-54 (2007). Also available as LHC Project Report 985. 460 461 462 [4] V. 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