Angular distribution measurement of atoms evaporated from a resistive oven applied to ion beam production
AAngular distribution measurement of atomsevaporated from a resistive oven applied to ionbeam production
A. Leduc , , T. Thuillier , L. Maunoury , and O. Bajeat Univ. Grenoble Alpes, CNRS, Grenoble INP ‡ , LPSC-IN2P3, 38000 Grenoble,France GANIL, bd Henri Becquerel, BP 55027,F-14076 Caen, FranceE-mail: [email protected]
January 2021
Abstract.
A low temperature oven has been developed to produce calcium beamwith Electron Cyclotron Resonance Ion Source (ECRIS). The atom flux from the ovenhas been studied experimentally as a function of the temperature and the angle ofemission by means of a quartz microbalance. The absolute flux measurement permittedto derive Antoine’s coefficient for the calcium sample used : A = 8 . ± .
07 and B = 7787 ±
110 in standard unit. The angular FWHM of the atom flux distributionis found to be 53 . ± . ° at 848K, temperature at which the gas behaviour is noncollisional. The atom flux hysteresis observed experimentally in several laboratories isexplained as follows: at first calcium heating, the evaporation comes from the sampleonly, resulting in a small evaporation rate. once a full calcium layer has formed onthe crucible refractory wall, the calcium evaporation surface includes the crucible’senhancing dramatically the evaporation rate for a given temperature. A Monte-Carlocode, developed to reproduce and investigate the oven behaviour as a function oftemperature is presented. A discussion on the gas regime in the oven is proposed asa function of its temperature. A fair agreement between experiment and simulation isfound.
1. Introduction
This work is dedicated to the study of a low temperature metallic oven dedicatedto calcium beam production at the SPIRAL2 facility at GANIL, France [1, 2]. Themotivation of the study is to better understand the physics and chemistry of such an ovenwith the goal to improve the global conversion efficiency of rare and expensive isotopeatom (like Ca) to an ion beam in Electron Cyclotron Resonance Ion Source (ECRIS).This study is the first step of longer term plan to build an end-to-end simulation ableto optimize and predict the atom to ion conversion yield of oven to produce beamsin ECRIS. Here, the differential atom flux from the oven is measured and compared ‡ Institute of Engineering Univ. Grenoble Alpes a r X i v : . [ phy s i c s . acc - ph ] F e b to simulation. Indeed, the angle of atom emission is an important geometrical factorof the whole atom to ion conversion in an ECRIS. In a first part, the calcium ovenused is presented in detail. In a second part, the experimental setup used to study thedifferential atom flux from the oven is described. Next, the Monte Carlo model used tosimulate the oven behaviour is presented and the simulation results discussed. In thelast section, simulation and experimental results are compared and discussed. Figure 1. (A) Calcium oven cut away view . (B) Detailed view of the cruciblein light purple.
2. Calcium oven
The oven design is derived from an existing technology developed at Lawrence BerkeleyNational Laboratory [3]. A cutaway view of the oven is presented on Fig.1 withinformation on its mechanical composition. The oven crucible is made of molybdenum toprevent chemical reaction with the metallic sample. The crucible cavity has a symmetryof revolution and is composed of two parts (see view B of Fig.1): (a) a 5mm diameterand 11 mm long cylindrical container ending on the last millimeter by a 30 ° cone (shapeimposed by the drilling tool geometry), (b) an 1 mm diameter and 2 mm long extractionchannel (also referenced later as a nozzle). The oven is heatable up to 875K when aJoule power of 200W is applied. A thermal simulation done with Ansys software hasshown that the crucible temperature is very homogeneous with a maximum temperaturegradient of the order of a few degrees Kelvin only. Figure 2.
Cutaway view of the vacuum chamber, the rotatable quartzmeasurement system (blue) and the oven tested (red)
3. Experimental measurements
The oven metallic atom emission has been measured in a dedicated vacuum chamber (seeFig. 2) with a residual pressure P = 10 − mbar. The oven temperature is monitored bythe thermocouple included in the oven heater cartridge. The atom flux is measured witha quartz AUDA6 Neyco micro balance. The quartz is inserted into a mechanical supportresulting in an active measurement disc diameter of 8.1 mm. The quartz temperature isfixed thanks to a water cooling system. The vertical support is mechanically connectedto a rotatable vacuum flange by means of a tube bringing water cooling to the balance.the tube is bent to form two 90 ° bends so that during a rotation, the quartz describes acircle with a 60 mm radius. The crystal frequency of vibration is 3 MHz when a staticelectric field is applied. When evaporated metallic atoms are deposited on the quartzsurface, its mass increases and thus changes its mechanical resonance frequency. Thequartz frequency measurement is done with a dedicated Inficon controller which displaysthe instantaneous frequency and calculates the mass per cm accumulated during aprogrammable integration time. During the experiments, the mass flux is calculatedafter an integration time from 60 to 180 s. In our experimental conditions, The masslimit accuracy of the system has been estimated to be ≈ . ng/cm /s . The oven axisis horizontal and set perpendicular to the balance axis of rotation. The oven positioncan be translated along the direction of its axis of revolution. The two experimentalconfigurations reported are displayed on Fig.3. In the configuration (1), the oven exit isplaced on the balance axis of rotation. During the quartz rotation, the distance betweenthe oven and the quartz is constant and equals to 60 mm. The angle between the quartzsurface and the oven surface is noted θ . In the configuration (2), the quartz is set 10mm away from the oven exit. The solid angle covered by the quartz is then ≈ θ = 22 , ° . Figure 3.
Sketch showing the positions of the quartz balance during the experiments.(1) The quartz describes a circle of radius 60 mm around the oven exit. The quartzand the oven axis form an angle with − π/ ≤ θ ≤ π/
2. (2) The quartz is set 10 mmaway from of the oven hole.
Table 1.
Mass flow and FWHM measurements from protocol (2) (see Fig.3). element T (K) ˙ M ( ng/s ) FWHM (deg.)Ca 848 148.9 ±
67 53.7 ± ±
67 55.5 ± ±
67 62.3 ± The oven run presented used a calcium 40 sample weighting 0.0909 g with a surface s Ca = 0 . ± . cm . The overall crucible internal surface is s c = 2 . cm . The differentialmetallic mass flow emitted by the oven: f ( θ ) = 1 r d ˙ mdω (1)was measured as a function of θ at T=848, 873 and 898 K (see protocol (1) inFig.3). Here r is the radial distance between the oven and the balance and dω standsfor the differential solid angle taken at θ . Results are displayed in fig.4. The errorbar on θ is due to the extended surface of detection ( σ θ = 0 . ° ), the error on angle measurement( σ θ ≈ ° ) and the error on alignment ( σ θ ≈ . ° ), leading to a global error σ θ ≈ . ° .The mass flux measurement precision is limited by the resolution of the balance forthe chosen time of integration of 180 s. The mass flux error is thus estimated to be σ ˙ m ≈ . ng/cm /s . The full width half maximum (FWHM) of the distributions arereported in Table 6, along with the reconstructed total mass flux ˙ M integrated over 2 π sr (and opportunely averaged on the overabundant range of measurement from − π/ π/
2) : ˙ M = 2 πr (cid:32) (cid:90) π/ f ( θ ) sinθdθ + 12 (cid:90) − π/ f ( θ ) sinθdθ (cid:33) (2)The angular FWHM values are consistent for all data (FWHM 53-63 ° ). Furtheranalysis of the angular mass flow distribution is proposed later in the text helped with aMonte Carlo code. Next, the calcium evaporation rate was measured as a function of theoven temperature in the experimental condition (2) (see Fig.3). The total calcium fluxis reconstructed as a function of the temperature using the experimental measurementof f ( θ ), by applying the following correcting factor: (cid:82) θ f ( θ ) sinθdθ (cid:82) π/ f ( θ ) sinθdθ = 5 .
565 (3)where f is taken for T=898K, when the precision of experiment (1) is the highest.The experimental data is plotted with blue errorbars on fig. 5. The other solid colorplots on fig. 5 are discussed later in the text.
4. Oven thermodynamics and analysis
Table 2.
Calcium Antoine’s equation coefficient according to [4] and calculated inthis study, expressed in standard units.
A B CCa from [4] 10 .
34 8 . × . ± .
07 7 . ± . × . mm ) is small compared to itsinternal total surface ( s c = 2 . cm ). See fig.3, view B to visualise the difference. Thecavity is thus sufficiently closed to consider it as a Knudsen cell[5, 6]. Consequently,when the metal sample is heated, the local pressure in the crucible raises rapidly to reachthe saturating vapor pressure, well above the residual pressure of the vacuum chamber Figure 4.
Experimental flux emitted from the oven as a function of the angle θ forcalcium. The black, red and blue plots are respectively measured at the temperatures850, 875, 900 ° K. ( P = 10 − Pa). The calcium saturation vapor pressures P (Pa) follow the Antoine’slaw as a function of the temperature : log P = A − BC + T (4)where T ( K ) is the metal temperature and A, B, C are thermodynamics parameters,unique for each chemical element. The evaporated mass rate ˙ M emitted from the solidmetal in the crucible can be expressed using the Hertz-Knudsen equation[7, 8] :˙ M = P (cid:114) m πkT S (5)where m is the atom mass, P is the metal saturating vapor pressure and S is thesurface of evaporation. Another important oven parameter is the sticking time of atomson the hot crucible surfaces defined by the Frenkel equation[9]: τ = τ e HkT (6)where τ ≈ − s is the atom vibration period on the surface [10], H is the enthalpyof the adsorbed atom, k the Boltzmann constant and T the surface temperature. For Figure 5.
Total calcium flux from the oven as a function of the temperature. Bluesymbols: experimental data. Red: theoretical data with S = s + s c and Ca data from[4]. Orange: least mean square fit of experimental data using S = s + s c and Antoine’slaw (see. Eq. 4) coefficients A and B as fit parameters the calcium case, two sticking times must be considered. the first is τ Ca − Ca , the stickingtime of calcium atom on the metallic Ca surface sample. the other is τ Ca − Mo , thesticking time of Ca on Mo. The adsorbed Ca enthalpy on Ca is well documented : H Ca = 1 . eV , giving a sticking time of 1 − ms for T − K . On the otherhand, the adsorbed Ca on Mo enthalpy value H Ca − Mo was not found in the literature.Nevertheless, H Ca − Mo is expected to be much higher than H Ca . A rough estimate of H Ca − Mo value can be considered from H Sc − Mo = 5 . eV available in [11]. In the presentexperimental conditions, τ Ca − Ca (cid:28) τ Ca − Mo on all the temperature range covered. Hence,when the calcium evaporation starts, a layer of calcium should first be formed on theMo crucible wall and stay stuck on Mo. Once the layer is complete, next Ca adsorptionon the surface is done on Ca, which strongly reduces the sticking time and transformsthe crucible surface to a fresh extra source of calcium. Two experimental confirmationsof this phenomenon have been observed: (i) at first start, the calcium flux is very smallfor a given temperature and, after a sufficiently long time of operation (of the order ofan hour), the flux amplifies to reach a much higher stable value. (ii) Immediately afterventing the oven used and inspecting its crucible, the presence of a Ca layer is visible onthe crucible surface which very rapidly get oxidised to form a white CaO powder. Thishypothesis is further investigated helped with the experimental data from experiment(1) (see Fig.3). The theoretical mass flow expected from Eq.4 and Eq.5 using Ca datafrom [4] is calculated for the temperatures 848, 873 and 898 K, considering the twoevaporating surfaces S = s and S = s c + s and reported in Tab. 3 along with theexperimental mass flow from Tab. 1. Clearly, one can see that the sole metal sampleevaporating surface (column with S = s ) is insufficient to reproduce the total massrate from the oven. But when the crucible surface is added (column with S = s c + s ),the matching between theory and experiment becomes very close. The measurementconfirms the hypothesis of the transient formation of a Ca layer on the crucible surfacewhich, once completed enhances the evaporation proportionally to the crucible surface. Table 3.
Theoretical integrated Mass flow from the oven in (ng/s) derived from Eq.4and 5, compared with the experimental flux for T=848, 873 and 898K.
T P ˙ M ( s ) ˙ M ( s + s c ) ˙ M Exp.( ° K) (Pa) ng/s ng/s ng/s848 0.627 47.7 179 148.9 ± ± ± ° C (873K). Above this value, experimental flux is lower than the semi-empirical prediction. Because the total flux has been reconstructed with a sufficientlyhigh precision, alternative Antoine’s coefficients are proposed for calcium to fit the dataresulting in the orange solid line. The fit value found for the whole temperature rangeare A = 8 . ± . B = 7787 . ±
110 and C = 0 in standard units.
5. Monte Carlo Simulation
The atom angular distribution from the oven has been investigated by means of a MonteCarlo simulation and compared with the experimental data. The exact 3 dimensionscrucible geometry is considered. The oven temperature T is a free parameter and isassumed to be uniform over all the crucible. The metallic sample geometry is notmodelled and the initial atom emission position is done randomly along a line followingthe bottom part of the crucible part (a). The atom emission from the wall follows theLambert’s cosine law: P ( θ ) = cosθ (7)where P ( θ ) is the probability of emission at an angle θ with respect to the local normalto the wall. A special care must be taken to inverse this probability distribution functionappropriately to use it safely in the Monte-Carlo code[12]. Because the atom emissionfrom the wall is done in a cavity with convex walls, a test is added in the code to checkif a fresh reemission occurs toward the cavity and not to the wall. The atom velocity istaken as the mean thermal velocity: v = (cid:115) kTm (8)where m is the considered atom mass. No accomodation from the wall is consideredas particles are assumed to be isothermal. Each new adsorption at the wall is countedand re-emission is immediate using the cosine law. The pressure in the part (a) of thecrucible is considered constant at the saturating vapor pressure P of eq.4. The pressurein the extraction channel (b) is assumed to decrease linearly from P down to the vacuumchamber pressure P = 10 − Pa. The atom collisions are modelled in the crucible usingthe atom mean free path λ : λ = kT √ πl P (9)where l is the atom diameter ( l ≈ pm for calcium). At each time step, the localpressure is considered and a random number is generated to check whether the atomcollides or not. In case of collision, a new atom velocity direction is randomly generatedon a uniform sphere. The metallic gas regime in the oven can be assessed with theKnudsen number: K = λd (10)where d is a characteristic length of the system studied. When K > .
5, the gas iscollisionless and atoms exiting the oven are directly those emitted from the walls. Anintermediate regime occurs when 0 . < K < . K < .
01, the gas becomes fully collisional and the effectfrom the wall is secondary. In our case, the crucible has 2 characteristic lengths andhence two Knudsen numbers: K i = λd with d =5 mm for the main cylinder and K ii = λd with d =1 mm for the crucible exiting channel. In this latter case, we considered themean pressure in the exit channel ( P + P ) to calculate λ . The evolutions of λ , K i and K ii are proposed as a function of T and P in the table 4. For the measurementsperformed on calcium up to 900K, one can deduce that the calcium gas behaviour ismainly non-collisional. Nevertheless, for T=900K, K i = 0 .
63 is at the threshold andcollision effect, thought not dominant should start to play a role. At 1000K, the calciumgas is collisional in the bulk area (a) while it remains above the transition in the exitingchannel. a fully developed collision regime is reached at 1100K with K ii = 0 .
12. Thedifferential angular distribution of exiting atom per unit of solid angle is displayed inFig.6 as a function of the temperature. The number of particles generated to producethe curves is 1 million. One can clearly see the transition from the non collisional regimeat 600K (see black curve) to the intermediate regime at 1000K where the bulk crucible iscollisional while the exit channel is not (see orange curve) and finally above 1100K wherethe whole oven volume is collisional and the extraction emittance is finally defined by thesole exiting channel geometry (see blue and purple curves). The associated normalizeddistribution of axial and radial exiting atom velocities are reported on Fig. 7 and 8respectively as a function of the oven temperature. The convention of color is identicalas for Fig.6. One can note how the exit channel geometry favors the atom emission inthe non-collisional regime 20 ° around the z direction (oven axis), while this conditionis destroyed above a temperature of 1000K.0 Figure 6.
Normalized differential distribution of atoms at the exit of the oven perunit of solid angle as a function of θ for different temperatures: 600K (black), 900K(red), 1000K (orange), 1100K (blue), 1200K (purple). Figure 7.
Normalized distribution of atoms velocity at the exit of the oven alongthe direction z for different temperatures: 600K (black), 900K (red), 1000K (orange),1100K (blue), 1200K (purple). Table 4.
Evolution of the atom mean free path λ and the two Knudsen numbers K i , K ii for the calcium oven as a function of the temperature T and the saturating vaporpressure P . T P λ K i K ii (K) (Pa) (m)600 2 . × − . × − . × − . × − Table 5.
Evolution of the mean number of atom bounces, volume collision anddistance travelled by an atom before its extraction from the oven as a function ofthe temperature.
T (K) bounces collisions distance (m)600 687 0.01 2.75700 686 2.03 2.77800 690 55.8 2.80850 769 245 2.84900 816 998 3.211000 1699 18416 7.021100 3291 2.89 × t = d/v + bτ e HkT (11)where b is the mean bounce number, v and d the mean atom velocity and distancetravelled. The result is displayed in Fig.10. The time of extraction first decreasesrapidly between 600 to 850 K thanks to the reduction of the mean sticking time. Above850 K, the extraction time increases again as now the process is dominated by the meandistance travelled which increases faster than the mean atom velocity.2 Figure 8.
Normalized distribution of atoms velocity at the exit of the oven alongthe direction x for different temperatures: 600K (black), 900K (red), 1000K (orange),1100K (blue), 1200K (purple).
Figure 9. (Black) Mean number of atom adsoption on the crucible wall before atomextraction. (Dashed Black) Number of volume collision in the oven before extraction.
Table 6.
Comparison between FWHM (in degree) of angular differential mass fluxmeasurements and simulation for calcium.
T (K) exp. ( ° ) simulation ( ° )848 53.7 ± ± ± ± ± ± Figure 10.
Estimated mean time to extract an atom from the oven as a function oftemperature.
Figure 11.
Comparison between the experimental differential mass flux measured inthe micro-scale and the Monte-Carlo simulation at T=898K.
6. Comparison of simulation and experiment
The oven Monte Carlo code is used to simulate the theoretical atom flux expected onthe micro scale as a function of the angle θ (see fig.3). An example of the comparisonbetween simulation and measurement is proposed on Fig.11. The simulation reproduceswell the general shape of the differential flux as a function of the angle θ . A discrepancyis nevertheless visible for angle larger than 45 ° where the measurements are higher thanthe simulation. the difference is nevertheless included in the error bar. The differentialflux FWHM is calculated for the simulation and compared with the experimentalmeasurements. The results of the simulation are consistent with the measurements. theexperimental FWHM is always higher than the simulation. This systematic differenceis likely due to a non simulated physical effect. One could suggest for instance thatthe actual oven extraction geometry is not exactly as simulated, or that the atomflux continues to collide at the exit of the oven on the first mm. As a conclusion,The Monte Carlo code developed provides satisfactory results compard to experimentalmeasurements and will next be used to study the metallic atom capture in ECR ionsource plasma.5 Appendix A. Experimental data
The reconstructed experimental values of the total atom mass flux plotted in fig 5 arereported for convenience in the tableA1.
Table A1. total calcium mass flow as a function of the temperature for theconfiguration (2).
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