Microwave field distribution and electron cyclotron resonance heating processa)F. Consoli, L. Celona, G. Ciavola, S. Gammino, F. Maimone, S. Barbarino, R. S. Catalano, and D. Mascali Citation: Review of Scientific Instruments 79, 02A308 (2008); doi: 10.1063/1.2805665 View online: http://dx.doi.org/10.1063/1.2805665 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/79/2?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Modeling multiple-frequency electron cyclotron resonance heatinga) Rev. Sci. Instrum. 85, 02A914 (2014); 10.1063/1.4827540 The preliminary tests of the superconducting electron cyclotron resonance ion source DECRIS-SC2a) Rev. Sci. Instrum. 83, 02A334 (2012); 10.1063/1.3671746 Microwave to plasma coupling in electron cyclotron resonance and microwave ion sources (invited)a) Rev. Sci. Instrum. 81, 02A333 (2010); 10.1063/1.3265366 Fourth generation electron cyclotron resonance ion sources (invited)a) Rev. Sci. Instrum. 79, 02A321 (2008); 10.1063/1.2816793 Electron cyclotron resonance plasmas and electron cyclotron resonance ion sources: Physics and technology(invited) Rev. Sci. Instrum. 75, 1381 (2004); 10.1063/1.1675926

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Microwave field distribution and electron cyclotron resonance heatingprocessa…

F. Consoli,b� L. Celona, G. Ciavola, S. Gammino, and F. MaimoneLaboratori Nazionali del Sud, Istituto Nazionale di Fisica Nucleare, 95123 Catania, Italy

S. Barbarino, R. S. Catalano, and D. MascaliUniversità degli Studi di Catania, 95100 Catania, Italy

�Presented 31 August 2007; received 28 August 2007; accepted 14 October 2007;published online 30 January 2008�

In an electron cyclotron resonance ion source, ions are produced from a plasma generated andsustained by microwaves with a proper frequency. Some experiments showed that the plasmaformation, the consequent amount of particles extracted from the source, and the related beam shapestrongly depend on the frequency of the electromagnetic wave feeding the cavity. In order to havea better understanding of these phenomena, in this work we deal with the description of the motionof a charged particle inside the plasma chamber model of the SERSE ion source operating atINFN-LNS in Catania, the analysis being applicable to any similar apparatus. The electromagneticfields inside the vacuum filled chamber were determined theoretically and, together with propersimulations, their fundamental role on the particle motion, on their confinement, and on the energytransfer they are subjected to during their motion within the cavity is shown. © 2008 AmericanInstitute of Physics. �DOI: 10.1063/1.2805665�

I. INTRODUCTION

Important nuclear physics experiments already built andin construction all over the world, such as the SPIRAL2facility and the LHC and FAIR chains of accelerators, re-quire the availability of milliampere beams of high chargestate ions.1–3 This is the reason for the boost toward thebuilding of ion sources that can lead to the fulfilling of theserequirements. The electron cyclotron resonance �ECR�phenomenon is the base process employed in the most effec-tive sources of highly charged ions.4 The ECR ion sources�ECRISs� that are now under construction exploit the knowl-edge acquired by previous experiments, and their develop-ment is based on the improvement of the magnetic plasmaconfinement and on the plasma chamber dimensions andstructure.

Many experiments upon different ECRISs �Refs. 5 and6� proved that the performances of these sources can bechanged notably by means of even small variations of thefrequency of the electromagnetic wave feeding them. Thismeans that it is possible to improve the coupling between thefeeding waves and the confined plasma by properly tuningthe microwave supply. This is of great interest because itmay address the design of the new generation ECR ionsources and also because of the possibility to improve theexisting ones.

A proper study on this topic must take into account thespatial distribution of the confined plasma and that of theelectromagnetic field within the source chamber. Both of

these distributions are a function of each other, and this re-lationship can be effectively described by Fig. 1. Because ofits complexity, this problem of consistence between the twodistributions is a difficult task to afford at the moment in atypical large volume ECRIS both theoretically and numeri-cally. A numerical treatment should involve the use ofparticle-in-cell codes7 together with electromagnetic simula-tors able to solve and determine the microwave field in acavity in the presence of anisotropic and inhomogeneousplasma.

A simple approach to the problem, involving the electro-magnetic analysis of the source in vacuum, can give a pictureof the source behavior due to even very small percentagevariations of the feeding microwave frequency.

II. THEORETICAL TREATMENT

The first step of the study considered the lossless modelof the SERSE ion source at INFN-LNS,8,9 the analysis beingapplicable to any similar apparatus. Some simulations on thecavity by using both HFSS™ �Ref. 10� and CST MICRO-

a�Contributed paper, published as part of the Proceedings of the 12thInternational Conference on Ion Sources, Jeju, Korea, August 2007.

b�Electronic mail: consoli@lns.infn.it.FIG. 1. Self-consistence relation between electromagnetic field and confinedplasma.

REVIEW OF SCIENTIFIC INSTRUMENTS 79, 02A308 �2008�

0034-6748/2008/79�2�/02A308/5/$23.00 © 2008 American Institute of Physics79, 02A308-1

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WAVE STUDIOTM �Ref. 11� electromagnetic solvers al-lowed to find accurate results only up to 2 GHz. Because ofthe chamber dimension with respect to the excitation fre-quency, the numerical problem becomes very cumbersomefor higher frequencies and it leads to many difficulties in thedetermination of the electromagnetic field. Under the hy-pothesis of a vacuum filled cavity, the problem of the micro-wave generator coupling to the plasma chamber can be re-solved by means of a proper theoretical treatment. Thechamber was considered as an empty cylindrical cavity with65 mm radius and 450 mm length, with perfectly conductivewalls and fed by a WR62 rectangular waveguide excited inits first mode TE10 and placed off axis �see Fig. 2�:

ETE10= − Aiei�rf t�rf�ag

�sin���x − xA�

ag�y , �1�

where ag is the waveguide width, A is a constant related tothe waveguide power, � is the magnetic permittivity in

vacuum, and f rf=�rf / �2�� is the frequency of the wave feed-ing the cavity. A discrete number of eigenmodes can existinside the chamber, each of them characterized by its reso-nant frequency �see Fig. 3�. A further step of the study hasinvolved the accounting of the power losses in the aluminumcavity walls and the external loading of the source due to thefeeding waveguide. The field within the cavity may be deter-mined as superimposition of all the modes excited therein.9,12

In particular, for the TM modes we obtained

ETM = ei�rf tAc2�ag

L2�a �n,�,r

1

i� �rf

�n�r�−

�n�r�

�rf +

1

QL

·�n

�n�rxn�Jn+12 �xn��Re�In�

TM�Im�In�

TM� � � rxn�

aJn�� xn��

asin� r�z

L sin n�

cos n� e�

+rn

�Jn� xn��

asin� r�z

Lcos n�

− sin n� e� −

Lxn�2

�a2 Jn� xn��

acos� r�z

L sin n�

cos n� ez� , �2�

where �n is Neumann’s factor �equal to 1 for n=0, equal to 2if n=1,2 , . . .�, xn� is the � root of the Bessel function of norder, fn�r=�n�r / �2�� is the mode resonance frequency inthe cylindrical cavity,12 and

In�TM = − �

S0

sin���x − xA�ag

���e−i�n+1��Jn+1� xn��

a + e−i�n−1��Jn−1� xn��

a�dS

�3�

gives the mode coupling to the feeding waveguide, wherethe integration is performed over the waveguide section S0.

It is related to the power coupled from the waveguide toeach mode, and it also resolves the mode rotation due to thegeometrical degeneration caused by the cavity axial sym-metry.9,12 Furthermore, the mode resonance frequency whenthe wall losses were considered is

�n�r� = �n�r�1 −1

2Q , �4�

where Q is the unloaded quality factor calculated for eachmode in the aluminum cylindrical cavity. In the more generalcase of a cavity filled with a lossy medium, it is important totake into account the medium conductivity to determine thetrue mode frequency shifting. The external Q factor �Qext�accounts for the loading of the feeding waveguide to the

FIG. 2. Scheme of the injection flange of the cylindrical cavity with thefeeding waveguide; a=65 mm, L �cavity length�=450 mm, ag=2bg

=15.8 mm, xA=−40.4 mm, yA=−28.95 mm.

FIG. 3. �Color online� Frequency distribution of the resonant modes in thelossless cylindrical cavity representing the plasma chamber.

02A308-2 Consoli et al. Rev. Sci. Instrum. 79, 02A308 �2008�

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cavity,12 and the loaded Q �QL� is determined by both ofthem:

1

QL=

1

Q+

1

Qext. �5�

We suppose that the microwave source is connected to thechamber through a proper variable lossless matching net-work. Therefore, we can consider it as perfectly matched tothe cavity when we excite one of its resonant modes. Underthese conditions, it is possible to find QL=Q /2.12,13 Simi-larly, for the TE modes:

ETE = ei�rf tAc2�ag

L2�a �n,�,r

1

i� �rf

�n�r�−

�n�r�

�rf +

1

QL

��nrxn��

�n�r�xn��2 − n2�Jn

2�xn�� �Im�In�TE�

Re�In�TE� sin� r�z

L

� �n

�Jn� xn�� �

acos n�

− sin n� e� −

xn��

aJn�� xn�� �

a

� sin n�

cos n� e�� , �6�

where xn�� is the � root of the derivative of the Bessel func-tion of n order and

In�TE = �

S0

sin���x − xA�ag

���− ei�n+1��Jn+1� xn�� �

a + ei�n−1��Jn−1� xn�� �

a�dS

�7�

represents the mode coupling to the waveguide. The positionof the waveguide, its dimensions, and the microwave fre-quency are fundamental parameters for the determination of

the electromagnetic field within the chamber, as a superim-position of the many modes excited therein. The field wasobtained under the hypothesis that it is possible to exciteeach mode independently from the others, and therefore thatno coupling is present among them. In the case of strongmode coupling, it is necessary to redefine the consideredmode set in order to preserve the mode orthogonality in theHilbert space.13 This is beyond the scope of the presentwork, and when the excited mode is strongly coupled to theothers, Eqs. �2� and �6� have been considered here as ap-proximated field representation. In Fig. 4 the electric fielddistributions in the z=233 mm plane is shown when thelossy cavity is excited at the frequency of one of its resonantmodes and with 1 W of normalized input power. It is evidentas different modes notably contribute to the total field whenthe characteristic frequency of the TE4 4 23 mode is consid-ered. It is clear that the pattern and the maximum electricfield change completely even for very small percentagevariations of the feeding wave frequency �around 1 MHzover 14 GHz�. It notably affects both the spatial distributionof minima and maxima and the amount of energy coupledfrom the waveguide to the cavity.

The electromagnetic field under these conditions isclearly different from that present in the cavity filled with theconfined plasma, but we think that its dependences on thefrequency variations of the feeding wave, as well as on thephysical characteristics of the excitation structure, arepresent at some extent also in the last more complex case, asit is indicated by the experiments.

III. SIMULATION OF THE PARTICLE MOTIONIN THE CAVITY

The SERSE cavity is surrounded by a magnetic structureproducing a magnetostatic field suitable to confine particles,which in the plasma chamber can be described as generatedby the superimposition of a hexapole and two solenoids:

Bx = x�− B1z + 2Sexy�, By = − B1yz + Sex�x2 − y2�,

Bz = B0 + B1z2, �8�

where Sex=310 T /m2 is a constant related to the hexapolefield, and B0=0.5 T and B1=50 T /m2 are related to the so-lenoid ones. The particles inside the ion source cavity aretherefore subjected to a nonuniform confining magnetostaticfield B. We determined analytically the ECR surface, where

FIG. 4. �Color online� Modulus of the electric field in the planez=233 mm when the cavity is excited at the frequency of one of its resonantmode, normalized to 1 W of input microwave power.

FIG. 5. �Color online� Field distributions on the relative ECR surface whenthe cavity is excited at the resonance frequency of one of its modes.

02A308-3 Cavity field distribution, ECR process Rev. Sci. Instrum. 79, 02A308 �2008�

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the condition �rf=�g=qBECR /m holds. It is obtained by theequation A1�4+A2�2+A3=0, where14

A1 = B12 cos2 + Sex

2 sin4 − B1Sex sin2 sin 2 sin 3 ,

A2 = 2B0B1 cos2 ,

A3 = B02 − �m�/q�2. �9�

The electromagnetic field distribution on this surface for twomodes close to the frequency of 14 GHz is plotted in Fig. 5.It is evident that some mode configurations can have a verylow field on the surface, and it considerably affects the ECRprocess. Under these conditions, we resolved numerically theparticle motion equation:

dv

dt=

q

m0��E + v � B −

v · E

c2 v� , �10�

with �= �1− �v /c�2�−0.5, where c is the velocity of light invacuum, and q and m0 are the particle charge and mass. Weevaluated the trajectory, the energy, and the confinement ofthe electrons in a 50 ns time interval. For the sake of sim-plicity, we consider each time the presence of only one elec-tron inside the cavity, which in every point is subjected to thesuperimposition of both the magnetostatic and the electro-magnetic field. The cavity is excited at the resonance fre-quency of the TE4 4 23 mode, with a 2000 W power. In Fig.6 the energy evolution of the electron with time is shown�the initial conditions are x=0.01 m, y=0 m, z=−0.05 m,vx=5�107 m /s, vy =0 m /s, vz=5�107 m /s�. In this figure,the regions where the electron is in proximity of the ECR

surface, i.e., where the magnetic field Bp applied to the elec-tron satisfies the condition �1− �BP /BECR���0.1, are outlined.It can be observed that the energy exchange between fieldsand electron occurs in these regions. In Fig. 7 the electronmotion is shown with respect to the ECR surface. In particu-lar, it is shown that in this case the electron crosses the sur-face in the presence of a high electromagnetic field.

For this field configuration, we considered a large num-ber of single-electron motion simulations, taking the velocityof these particles with Maxwellian distribution and averageenergy around 500 eV, again with a simulation time of 50 nsand a net power of 2000 W flowing from the waveguide tothe chamber. In order to take into account the effect of theelectromagnetic field on the particle motion, this set of simu-lations was repeated applying to the particles each time adifferent field distribution, obtained when the lossy cavity invacuum is excited at the resonance frequency of one of itsmodes. The results obtained for the different fields are sum-marized in Table I and shown in Fig. 8. The importantchanges described by Fig. 4 on the field pattern even for verysmall frequency changes affect the trajectory, the confine-ment, and the average energy of the particles moving withinthe cavity. The average energy gain can be increased fromaround 1 to more than 30, depending on the applied micro-wave frequency. The percentage of confined particles afterthe simulation time is dependent on the energy transfer effi-ciency between the electromagnetic wave and electron, and it

FIG. 7. �Color online� Electron motion and modulus of the electric fieldapplied on the ECR surface.

FIG. 6. �Color online� Electron energy vs time. The vertical rectanglesindicate the positions where the condition �1− �BP /BECR���0.1 holds.

TABLE I. Effects of different field configurations on the electron motionwithin the source chamber when the cavity is excited at the resonance fre-quency of one of its modes in terms of the number of confined particles,average energy, and gain.

fn�r

�MHz�Energy�keV�

Energygain

No. ofconfined

electrons �%�

TE1 4 33 13 952.354 13.110 24.97 95TE3 2 38 13 958.445 11.892 22.65 93TE6 2 33 13 965.417 2.601 4.95 93TM5 4 4 13 995.897 0.531 1.01 88TM9 1 30 13 998.329 0.562 1.07 87TE4 4 23 14 000.643 3.932 7.49 95TE3 1 41 14 000.964 3.245 6.18 92TE1 1 42 14 055.391 17.793 33.89 95No e.m. field 0.525 83

FIG. 8. �Color online� Final average electron energy after 50 ns simulationtime for the field configurations obtained when the cavity is excited at thefrequency of one of its modes.

02A308-4 Consoli et al. Rev. Sci. Instrum. 79, 02A308 �2008�

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is caused by the particles plugging in due to the electromag-netic field.4,15 In our study, the net power flowing into thechamber is kept constant, and therefore the observed effectsare only due to the different field patterns. Moreover, weconsidered the case when the cavity is excited at the reso-nance frequency of the TE3 1 41 and with 4000 W inputpower. In this case the average energy is 4.824 keV, the gainis equal to 9.2, and there is 94% fraction of confined elec-trons. The gain therefore increased about 50% with respect tothe same case with 2000 W power only. This result meansthat a correct tuning of the cavity may increase the averageelectron energy remarkably.

IV. DISCUSSION

In this work we have shown the effects of the electro-magnetic field on the motion of an electron in vacuum in aconfining magnetostatic field proper of the ECRIS. Thechange in the field pattern at a constant input power notablyaffects the energy and the confinement of the particles. Thesevariations are encountered even for very small frequencypercentage changes.

The problem of determining the electromagnetic fieldwithin a cavity where anisotropic inhomogeneous plasma ispresent is far more complex to resolve than in the presentcase, and in principle in some cases, a clear modal structurecould also be not present. However, the conclusions derivedin this simpler case can be applied to some extent also to theother one. A change in the field pattern would determine achange in the energy transfer between microwave field andparticles that would also affect the plasma confinement andthe electron energy distribution, as it was experimentallyobserved.6

The frequency tuning of an ECRIS seems to be an effec-tive way to improve the source performances while keepingthe feeding wave power constant, as it was observed in Ref.5 and applied since then in the CNAO ion sources. Ofcourse, it is important to understand how these observed phe-nomena can influence the parameters of the confined plasmaand how they can be affected by them in terms of confiningmagnetic field, cavity wall outgassing, average particle en-ergy, and concentration. This is an important topic because

the optimization of the coupling between microwaves andplasma is one of the key points for the development of moreoutstanding new generation ion sources, as well as for theimprovement of the existing ones.

ACKNOWLEDGMENTS

The work is supported by EURONS �European Commis-sion Contract No. 506065� and by the Fifth National Com-mittee of INFN �INES experiment�.

1 W. Barth, L. Dahl, L. Groening, S. Yaramishev, and U. Ratzinger, inProceedings of the XXIII International Linear Accelerator Conference�LINAC 2006�, Knoxville, TN, 21–25 August 2006 �ORNL, Oak Ridge,2007�, p. 180.

2 T. Junquera, P. Bertrand, R. Ferdinand, and M. Jacquemet, in Proceedingsof the XXIII International Linear Accelerator Conference �LINAC 2006�,Knoxville, TN, 21–25 August 2006 �ORNL, Oak Ridge, 2007�, p. 142.

3 N. Angert, P. SpädtkeC. Hill, H. Haseroth, A. Girard, D. Hitz, P. Ludwig,G. Melin, J-L. Bouly, J-F. Bruandet, N. Chauvin, J-C. Curdy, R. Geller, T.Lamy, P. Sole, P. Sortais, J-L. Vieux-Rochaz, G. Ciavola, S. Gammino,and L. Celona, in Proceedings of the 14th International Workshop on ECRIon Sources, ECRIS99, CERN, Geneva, Switzerland, 3–6 May 1999,CERN Report CERN/PS/99-52 �HP�, 1999, p. 220.

4 R. Geller, Electron Cyclotron Resonance Ion Sources and ECR Plasmas�IOP, Bristol, 1996�.

5 S. Gammino, High Energy Phys. Nucl. Phys. 31�S1�, 137 �2007�.6 L. Celona, G. Ciavola, F. Consoli, S. Gammino, F. Maimone, P. Spädtke,K. Tinschert, R. Lang, J. Mäder, J. Roßbach, S. Barbarino, R. S. Catalano,and D. Mascali, “Observation of the frequency tuning effect in the 14 GHzCaprice ECR ion soruce,” Rev. Sci. Instrum. �submitted�.

7 C. K. Birsdall and A. B. Langdon, Plasma Physics via Computer Simula-tion �IOP, Bristol, 1991�.

8 F. Consoli, S. Barbarino, L. Celona, G. Ciavola, S. Gammino, and D.Mascali, Radiat. Eff. Defects Solids 160, 467 �2005�.

9 F. Consoli, L. Celona, G. Ciavola, S. Gammino, F. Maimone, R. S.Catalano, S. Barbarino, D. Mascali, and L. Tumino, in Proceedings of theSeventh Mediterranean Microwave Symposium, Budapest, Hungary,14–16 May 2007, p. 345.

10 See http://www.ansoft.com/products/hf/hfss/11 See http://www.cst.com/Cottent/Products/MWS/Overview.aspx12 J. C. Slater, Microwave Electronics �Van Nostrand, Princeton, 1963�.13 K. Kurokawa, An Introduction to the Theory of Microwave Circuits �Aca-

demic, New York, 1969�.14 R. S. Catalano, F. Consoli, and S. Barbarino, “Analytical evaluation of the

expression and parameters of a resonance curve in an experimental ECRsetup,” Eur. Phys. J. D �in preparation�.

15 D. Mascali, R. S. Catalano, L. Celona, G. Ciavola, F. Consoli, S.Gammino, F. Maimone, S. Barbarino, and L. Tumino, in Proceedings ofthe 34th EPS Conference on Plasma Physics, Warsaw, Poland, 2–6 July2007.

02A308-5 Cavity field distribution, ECR process Rev. Sci. Instrum. 79, 02A308 �2008�

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