Study of a new cusp field for an 18 GHz ECR ion source

NIM B Beam Interactions with Materials & Atoms

Nuclear Instruments and Methods in Physics Research B 262 (2007) 95–104 www.elsevier.com/locate/nimb

Study of a new cusp field for an 18 GHz ECR ion source M.H. Rashid a

a,* ,

T. Nakagawa b, A. Goto b, Y. Yano

b

Variable Energy Cyclotron Centre, 1/AF-Bidhan Nagar, Kolkata 700 064, India b Nishina Cyclotron Centre, RIKEN, Wako, Saitama 351-0198, Japan Received 6 July 2006; received in revised form 16 May 2007 Available online 29 May 2007

Abstract A feasibility study was performed to generate new sufficient mirror cusp magnetic field (CMF) by using the coils of the existing room temperature traditional 18 GHz electron cyclotron resonance ion source (ECRIS) at RIKEN. The CMF configuration was chosen because it contains plasma superbly and no multipole magnet is needed to make the contained plasma quiescent with no magneto-hydrodynamic (MHD) instability and to make the system cost-effective. The least magnetic field, 13 kG is achieved at the interior wall of the plasma chamber including the point cusps (PC) on the central axis and the ring cusp (RC) on the mid-plane. The mirror ratio calculation and electron simulation were done in the computed CMF. It was found to contain the electrons for longer time than in traditional field. It is proposed that a powerful CMF ECRIS can be constructed, which is capable of producing intense highly charged ion (HCI) beam for light and heavy elements.  2007 Elsevier B.V. All rights reserved. PACS: 29.25.Ni; 52.55.Jd; 52.50.Sw; 52.25.Jm Keywords: ECR ion source; Minimum-B field; Cusp mirror field; Plasma confinement

1. Introduction The idea of producing multiply charged ions using electrons heated by electron cyclotron resonance (ECR) technique was first put into action by Geller’s group at Grenoble, France. They constructed ECR ion sources (ECRIS) like MAFIOS and its variants in 1970s and later [1–3]. The ECR plasma and its property have been described well by him [4] in terms of confinement of plasma, ECR heating and techniques to improve working of an ECR ion source. A comprehensive review of the technical developments and various types of ECR ion sources for various applications has been given in [5–8]. A minimum-B field (magnetic well) was produced employing axial field and radial magnetic field for *

Corresponding author. Tel.: +91 33 2337 1230x2420; fax: +91 33 2334 6871. E-mail address: [email protected] (M.H. Rashid). 0168-583X/$ - see front matter  2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2007.05.014

confining plasma quiescently. Henceforth, it will be referred to as traditional magnetic field (TMF) configuration. A vacuum chamber in such ion source is filled with three invisible components rarefied gas, microwave power and magnetic field lines. The cold electrons with some initial kinetic energy gyrate about a magnetic line of force (MLF) with certain frequency proportional to the magnetic field strength. If the frequency matches with the frequency of the injected microwave, electrons get energy from the microwave resonantly. Upgradation and improvement of ECR ion sources in terms of species, charge states and intensities has become indispensable in the modern age of advanced research in various fields. It is done using higher and higher magnetic field and microwave frequency in an ECR ion source to generate more intense ion beam of more common or rare species with higher charge state. Several activities around the world for improving production of more intense HCI beam are going on. The prevalent techniques [9] to improve

M.H. Rashid et al. / Nucl. Instr. and Meth. in Phys. Res. B 262 (2007) 95–104

the performance of advanced ECR ion source also include proper gas mixing [10], multiple-frequency plasma heating [11], placing negatively biased disk [12], chamber surface coating by aluminum oxide [13] and improved plasma confinement with higher magnetic mirror fields [14]. Some advanced TMF ECRIS’es [15,16] is in operation or under development at present. An ECRIS of more than 14.5 GHz frequency requires higher magnetic field for energizing cold electrons and confinement of plasma. It helps to achieve higher value of nesi for generating intense HCI beam. The superconducting ECR ion sources like, SERSE, GYROSERSE [17], DECRIS [18], SHIVA [19], RAMSES [20] and PKDELIS [21] function at high magnetic field. Traditional advanced ECR ion sources using minimumB field formed by axial solenoid field and the radial sextupole field have some problems like (i) the plasma generated is not axially symmetric along the length and causes aberration to the extracted beam, (ii) the magnet system is very complicated for generating axial as well as radial field, (iii) plasma volume is small for placing the sextupole, (iv) injection and extraction regions are very limited and congested and (v) vulnerable magnet system because of huge magnetic stored energy and stress. In this paper it has been attempted to alleviate the problems in an ion source by employing cusp magnetic field (CMF) configuration. Thus, the main motivating factors of the present study are (i) to study the possibility of more confinement of electrons for heating the electrons through ECR process, (ii) to produce pulsed or continuous beam of narrow or broad size and above all, (iii) to construct a simple, compact and costeffective ECRIS. More confinement of ions to strip them further of their electrons and production of dense large volume of plasma consisting of highly charged ions (HCI) follow mainly from the point (i). Many atomic processes take place in ECR discharged plasma but we now pay attention to two main processes to retain the simplicity for our understanding, which determine the number density of the HCI in steady state. They are ionization of neutral atoms and ions through stepwise stripping by fast electrons and charge exchange with neutral atoms [22]. Continuous loss of particles takes place to the wall in addition to the extraction of ion beam out of the chamber and injection of neutrals at pressure of the order of 107 mbar. The high frequency microwave power is injected at the injection side. The plasma is contained by the magnetic field and the electrostatic plasma potential generated inside the chamber. They reduce the loss on the wall and keep the particles for longer time in the plasma to increase the density and charge state. It is possible to obtain Eq. (1) in the steady state from the particle balance equation described in simple form in [22] ðQþ1Þ

Ni

=N Qi ¼ ðnf S Q;io Þ=ðN 0 S Q;ex þ ð1=si ÞÞ;

ð1Þ

where Ni is the number density of ions with charge state Q, SQ,io and SQ,ex are the probabilities of atomic ionization and exchange reaction rates, respectively. It is seen here

that high vacuum, i.e. low density of neutral atoms (N0) for reducing the rate of charge exchange, high density of fast electrons (nf) for causing successive ionization and long ion confinement time (si) for producing high charge state of ions are favourable for generating high density of HCI’s. The plasma density ne is deduced from ne 6 e0 me x2rf =e2 and given in per cc by ne 6 1:11  1010 frf2 in engineering notation, where the equality sign corresponds to the critical plasma density and the microwave frequency, frf is in GHz. The critical density versus frequency plot is depicted in Fig. 1. It is possible to get plasma densities of the order of 1011, 1012 or 1013 per cc at frequencies 9.5, 30 or 95 GHz, respectively. The standard model based on the experimental results for constructing a superbly functioning ECRIS, it is essential to meet the following criteria concerning the magnetic field achieved in the plasma chamber [16,23,24]; Bmax P 2BECR, Bmax = Binj P Bwall and Bext  Binj, where BECR = (f/2.8) kG and f is the microwave frequency in GHz; Bmax is the maximum magnetic field at the injection end and Bext is the magnetic field at the extraction end of the chamber. From empirical scaling laws of ECRIS [4,25] hQopi / Log(Bmax) and I Qþ / ðf 2 ne V p Þ= ðAai si Þ, where Vp is the plasma volume, Ai and si are the ion mass number and the ion confinement time at the extraction region. The parameter a has value close to 1. From these equations it is found if 50 lA of Ar8+ is extracted from 5 GHz ECRIS then 5 mA of Ar16+ will be extracted from 50 GHz ECRIS. The laws worked fairly good to address properly the design of new TMF ECRIS’es. Many advanced TMF ECRIS’es are under operation or construction. Several activities around the world for improving production of more intense beam of HCI of elements like Bi, U, etc. are going on. The VENUS [26,27] in the USA and the MSECRIS [28] in Europe are the fitting examples of the most powerful TMF ECRIS’es in operation and under development, respectively.

15

14

13 Log [ne /cc]

96

12

11

10

9 0

10

20

30

40

50

60

70

80

90

100

Frequency (GHz)

Fig. 1. The critical plasma density versus microwave frequency plot for estimation of plasma density.

M.H. Rashid et al. / Nucl. Instr. and Meth. in Phys. Res. B 262 (2007) 95–104

2. Cusp magnetic field A cusp is defined as a point of intersection of two arcs or curves at which either the tangents on the curves coincide or they are almost parallel. The scheme of the CMF generation is depicted in Fig. 2. It is generated using two coaxial coils of the same or different dimensions kept apart and energized oppositely. The positions of the point cusp (PC) and the ring cusp (RC) are shown on the surface of the plasma chamber as the tangents drawn on the MLF’s at these positions are almost parallel. The density of the MLF’s decreases towards the magnetic centre defined by the zero magnetic field inside the chamber. The magnetic centre in a cylindrically symmetric magnet system can move on the central axis depending on the structure and positions of the iron and coil as well as depending on the excitation of the two coils with unbalanced magnetomotive force. The magnetic centre coincides the geometrical centre when the system is axially and radially symmetric and the coils are just oppositely excited. The vector potential generated in the CMF configuration is given by Ah(r, z) = (B0/2z0)rz, where B0 is the magnetic field at z0 on the central z-axis. The radial and axial components Br and Bz, respectively of the field are given by the following Eq. (2). 0 1 0 1 0 1 oðrAh Þ=oz Br ðB0 =2z0 Þr B C 1B C B C ð2Þ @ Bh A ¼ @ 0 A ¼ @0 A r oðrAh Þ=or 2ðB0 =2z0 Þz: Bz The MLF’s constitute a surface which is represented by w(r, z) = rAh(r, z). The convex surface of w(r, z) faces the magnetic centre of the system and locus of the centre of curvature of the MLF’s are outside the plasma chamber. I-

RC

I+

97

From the Maxwell’s equation curl B = 0 in the current free region inside the chamber, it is possible to show with the help of Fig. 3 that the magnetic field decreases inward according to the formulae Bin = Bout(R  rout)/(R  rin), where R=OO 0 and rin and rout represent the radius of curvature of the two contour curves along the MLF. Thus, the CMF in this case generates so called modified minimum-B field. The magnetic field at the cusp region is controlled and enhanced by the flux density achieved. The magnetic field increases all around from the magnetic centre, which is the characteristic of a minimum-B field. Even under magnetic mirror action plasma as a fluid is able to flow across the MLF’s because of inter-particle continuous collisional diffusion. The variation of plasma pressure along the MLF’s depends on the magnetic field. The plasma pressure, Ppar = nekBTe (dominated by the hot electrons) generate currents that modifies the magnetic field and plasma shape, where kB is the Boltzmann constant. The gravitation-like inward force because of the nature of MLF’s in the CMF produce a MHD-stable configuration. Evaluation of MHD equilibrium and stability of the plasma is done from the fundamental equations j  B ¼ $P par , $  B ¼ l0 j and $  B ¼ 0, which yield the familiar pressure and field distribution and lead to Eq. (3) [4, p. 120]. The distribution of magnetic field leaves the mass of the plasma fluid consisting of charged particles constant and the MLF’s frozen into them [29]. $ðP mag þ P par Þ ¼ ð1=l0 ÞðB  $ÞB:

ð3Þ

The curvature force on the right side of the Eq. (3) causes azimuthal drift of the electrons due to their tangential velocity component [4, p. 100]. It is found to be small, hence Pmag + Ppar  const. So, the magnetic pressure (Maxwell stress), Pmag = B2/(2l0) and the particle pressure, Ppar, are the highest and lowest, respectively, on the

Chamber MLF

O

MLF

rin

Radius PC (A ’)

O MLF

Z-axis

PC (A)

R

MLF

rout

C

Chamber

I+

RC

θ dθ

I-

Fig. 2. The scheme of the cusp magnetic field (CMF) configuration in which the magnetic lines of force (MLF) converge at point cusp (PC) and ring cusp (RC) at the chamber surface on the z-axis and in the midplane passing through O, respectively. Electric currents I- impinges into and I+ emerges out of the sheet. The injection and extraction positions are on the left and right end of the chamber, respectively, on the z-axis.

B

O’

Fig. 3. The diagram to show CMF distribution inside the chamber for plasma confinement. O and O 0 are magnetic centre and the centre of curvature of MLF. C is the contour for taking curlB.

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chamber wall. Plasma particles remain at the low field region that is at and around the magnetic centre inside the chamber with maximum of the particle pressure. This is how the pressure balance represents the containment of plasma in the traditional or modified minimum-B field configuration. The magnetic field at the central region of the CMF is weak and the invariance principle of adiabatic magnetic moment of electron is not perfectly valid. The plasma density at 18 GHz or higher frequencies exceeds 1 · 1012/cm3, so the plasma enters into the highly collisional regime. The quasi-gas-dynamic confinement of plasma takes place [30] because of the collisions of the electrons with slow ions on their course of being lost. The quasi-gas-dynamic regime is characterized by very small mean free path of electrons under electron–ion collisions compared to the extent of the excursion of the electrons between the magnetic mirror plugs. The rate of filling the loss cone by electrons due to high collision frequency is more than the rate of electron-loss within. The averaged electron velocity distribution function remains isotropic in the filled loss cone. Then the non-adiabatic motion of electrons at the magnetic centre is insignificant [31,32]. 2.1. Past ECRIS using CMF For many ECRIS designer, the CMF configuration was a subject of fascination because of its inherent property of total MHD stability. Many tried to employ it for confinement of plasma generated by various methods including microwave discharge but had limited success. The earliest practical attempt in this regard was done by Sudlitz and his group at the Warsaw University, Poland [33]. They used the same classical CMF configuration using a pair of coaxial coils but without using high permeability magnetic material as yoke. So, they achieved very less magnetic field on the RC than on the PC on the central axis. There was not sufficient magnetic pressure to contain the plasma particles at the RC. The huge loss of plasma (electron) took place there. The plasma remained there starved of sufficient electrons. Moreover, the microwave power was injected radially, which was unable to reach the far region of resonance surface because of attenuation and dissipation of electromagnetic power at the resonance surface close to the injection point. Being failed on their bold endeavour to achieve sufficient HCI’s, they turned to the same TMF putting sextupole inside the coils and making the plasma chamber smaller than in the CMF configuration [34]. They had to decide to extract the desired current of HCI at more cost and complexity of the magnet system than before a = b = 4.2 cm and c = 3.1 cm. Very recent attempt to use the qualities of the CMF to contain plasma generated by feeding as high as 100 kW of pulsed microwave power at 37.5 GHz frequency is done by Zorin and his group [31]. They reported extraction of highly intense medium charged nitrogen, N3+ and N4+, beams only. They used very small magnet system and

plasma chamber with magnetic field 20 kG at the PC and 10 kG on the RC at mid-length. They have reported no N7+ beam and no HCI beam of other element either. 2.2. Present CMF ECRIS studies Some study has been done at Variable Energy Cyclotron Centre, Kolkata, India recently to generate sufficient and symmetric magnetic field at PC and RC positions employing iron yokes and plugs of optimized geometry. The results of magnetic field computation were reported in the Indian Particle Accelerator Conference [35] showing that a TMF 14.4 GHz ECRIS [36] can, on paper, be split into two CMF ECRIS’es; one using the same coils and the other using the same permanent magnets after rearrangement to generate the required improved CMF. There are two 18 GHz TMF ECRIS’es working at the RIKEN, Japan for feeding the LINAC and Ring Cyclotrons with high current HCI beam for acceleration. One of the ECRIS [37] has room temperature coil and capable of generating 13 kG field on the axis by energizing with maximum magneto-motive force (MMF) of 200,000 A-turn. This together with the permanent magnet sextupole satisfied the high-B mode condition as the ECR field at 18 GHz is 6.43 kG. The calculation was performed using POISSON code [38] whether employing the same coils but different yoke and plug structures made of iron, the sufficient CMF was achieved. In this case the coils were brought close to each other. They were only 5.5 cm apart. The length of the magnet reduced to overall length of 48 cm including the end yokes. Using the geometry with original coil structure shown in Fig. 4, it was possible to generate more than the desired field (13 kG) at the PC but less than (12 kG) at the RC position. The fields so generated on the inner surface of the chamber was studied and found that it hovered around 12 kG on some portion of BB 0 line. Thus, the fields achieved at the PC and RC was unequal (asymmetric) so different loss cones at the cusp positions. The closed ECR field surface of oblate spheroid was obtained well inside the chamber and around the magnetic centre, but field on the chamber surface fell short of satisfying the high-B mode condition. So, it is not a satisfactory achievement of the CMF generated. The mirror bouncing in the motion of electrons take place in the achieved CMF in between the PC and RC positions. The magnitude of the magnetic field must be improved by optimizing the positions and structure of the coils and the iron plugs and yoke in such a way that the loss cone angle is small and equal (symmetric) resulting in reduction of the particle loss at the cusp positions. Now the chamber cylindrical surface is brought to the dotted line, the new position at 7.2 cm radius. The midplug M is correspondingly extended close to the dotted line with appropriate surface modification. The vacant space created under the original coils due to exclusion of the sextupole and resizing of the plasma chamber is filled with another small coil to attain more MMF. A gap of 2 cm

M.H. Rashid et al. / Nucl. Instr. and Meth. in Phys. Res. B 262 (2007) 95–104

99

25

Y 20

Radius in cm

Y

Y M

15

10

B’

5

O’

B

P

P

A’

0 –20

O

–10

0

A 10

20

Z-axis in cm Fig. 4. The diagram of the cylindrically symmetric magnet system of 18 GHz ECRIS in RIKEN in which coils, MS and chamber are depicted in black, green and red colours, respectively. (For interpretation of the references in colour in this figure legend, the reader is referred to the web version of this article.)

is created between the main coils and the yoke Y on cylindrical region to accommodate additional coils to enhance the MMF by 13%. Optimization of the coil position and geometry of the plugs M and P was done to achieve the final geometry shown in Fig. 5 in which the length of the chamber is AA 0 = BB 0 = 15 cm. The coil configuration is now different from that of the earlier coils. The CMF so generated is shown in the 3D field plot in Fig. 6 on the boundary of the chamber, OABO 0 B 0 A 0 O and on the mid-plane radius OO 0 . Now the field achieved is well above 13 kG everywhere on the chamber boundary. It is very important to assess the magnetic field mainly at the cusp positions owing to the magnetic iron plugs M and P. They were replaced by air regions in the problem geometry and recomputation of the field was done keeping the other components same. It was found that the magnetic field at the RC position decreased by 57.7% giving 5.5 kG field only. The contribution of the plug M is considerable and so its placement is very crucial. The magnetic field at the PC positions on injection and extraction end decreased by 38.5% and 40.2% giving 8.0 kG and 6.0 kG, respectively. The field contributed by the plug P’s is less than the plug M but they are not less crucial than M. The coils and plugs on the extraction side can be manipulated to decrease the magnetic field at the extraction region to widen and open up the loss cone for facilitating the extraction of the HCI to boost its intensity. This affects a little decrease of magnetic field at the RC and pretty increase of the container magnetic field at the PC at injection side. The ECR field surface corresponding to 18 GHz in the designed CMF is depicted by the vertical ellipse in the r–z plane (oblate spheroid in the r–h–z three dimensions) in Fig. 5. But the ellipse in the r–z plane is horizontal that is along the central axis (prolate spheroid, usually

cigar shaped in the r–h–z three dimensions) in the case of TMF ECRIS. The dimensions of the plasma chamber (radius = 7.2 cm, length = 15.0 cm) and ECR surface spheroid (semi-axes a = b = 4.2 and c = 3.1 along x, y and z axes) are large enough because of the removal of the sextupole to contain more plasma and to couple more energy, respectively, to the electrons crisscrossing the surface. But the dimensions of the old plasma chamber (radius = 3.8 cm and length = 24.0 cm) and ECR surface spheroid (semi-axes a = b = 1.8 cm and c = 6.0 cm) were less comparatively because of the sextupole inside the coils. The chamber (plasma) volume and ECR surface area increased by more than 2 times approximately with respect to the values in the TMF old 18 GHz ECRIS. Now more microwave energy can be coupled to electrons to heat them on the large area of the ECR surface. The density of the fast electrons increases in this way. Possibly the cold electron density may increase as well. 2.3. Confinement time The ion confinement time is a function of the plasma volume (chamber volume), Vp, the total loss area on the chamber surface, Al, at the cusp region where the plasma particles continue to be lost and the ion sound p speed, Cs (m/s) = 0.6 (qTe/M), where q(Coulomb), Te(eV) and M(kg) are the ion charge, average electron temperature and the ion mass, respectively. They are related as in Eq. (4) according to [22]. si ðsÞ ¼ V p =ðAl C s Þ:

ð4Þ

If one would assume a given argon plasma in a conventional TMF, and a similar plasma (same electron and ion

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Fig. 5. The diagram of the anticipated total set-up of the 18 GHz ECRIS with magnet system to generate sufficient CMF. It includes the injection and extraction electrodes at A 0 and A, respectively and dashed ECR surface of oblate spheroid shape inside the plasma chamber. The biased disk and strips are also depicted at A 0 (PC position) and O 0 (RC position) inside the chamber.

temperature) in the CMF, then the ion confinement times will scale with plasma volume divided by the loss area. Calculation gives a plasma volume for TMF of 1.1 and for CMF 2.4 litre. The loss area for TMF is found to be 2.7 times larger than that for CMF. This would then give a substantial increase (a factor of 6) in the ion confinement time, off course in the assumptions of this model. The affect of the charge state, Q of ions is implicitly included in the ion confinement Eq. (4) mentioned above through Cs; it is based on a model either. Ions are unmagnetized and undergo many collisions over a gyration and the ions have the same average low temper-

ature (maybe Ti  1 eV). The si of different charge states for Ar ions deduced from measurements performed with the Caprice 10 GHz ECRIS have been reported in [39], which corroborated the theoretical value of si calculated using Eq. (5) that includes the ion charge state explicitly: pffiffiffi ne Z eff si ¼ 7:1  1020 LQ ln K A 3=2 ; Ti E

ð5Þ

P where ne, E, A, ln K and Z eff ¼ ð nQ Q2 Þ=ne are electron density, electric field, atomic mass, Coulomb logarithm and effective charge of the plasma, respectively. In case

M.H. Rashid et al. / Nucl. Instr. and Meth. in Phys. Res. B 262 (2007) 95–104

101

B’ O’

fi Magnetic

eld (kG)

B 16 14 12 10 8 6 4 2 0 7 6

A A ’

4

3

O

2

)

cm

( us di Ra

5

1 0

0 1 2 -4 -3 -2 -1 -8 -7 -6 -5 (cm) Central z-axis

3

4

5

6

7

8

Fig. 6. The 3D magnetic field plot on the boundary OABO 0 B 0 A 0 O of the plasma chamber and along OO 0 radius at the mid-length in Fig. 5.

one assumes the same plasma in TMF and CMF, then the ion confinement time, si will scale with the typical plasma length L, resulting in an improvement factor of about 1.5. The evaluated si is pretty longer in the designed CMF than in the old TMF ECRIS either using Eqs. (4) or (5). It is also found here that the order of the computed si using these equations is same that is millisecond. The computed si using Eq. (4) is less than using Eq. (5) only by a factor <5. The achievable plasma density in the 18 GHz CUSP ECRIS is more than 1 · 1012/cc, so the evaluated si from Eq. (5) will increase further. The formulae used above for calculating the si provide an idea of the importance of increasing the plasma size (volume), resonance zone extent L and decreasing the ion temperature Ti. 2.4. Electron simulation Loss of plasma particles takes place continuously on the chamber surface, but robust containment of particles (electron) in the chamber immersed in a minimum-B field reduces it and consequently increases the plasma density in the chamber. The improved CMF forms a bent magnetic bottle in between PC and RC, in which the force F = l$B restricts the motion of an electron of magnetic moment l in the direction of increasing magnetic field. In an ECRIS it is reasonable to define the loss cone only for electrons since ions are highly collisional and their velocity components is small and constantly changing. Here, the electron motion in the CMF generated is presented showing multiple mirror reflection of electrons for reducing the loss of electrons mainly at the PC and RC regions on the chamber surface. Electron simulation was done in the computed improved CMF taking various combinations of electron energy components Ee? and Eek with respect to the MLF followed by the electrons, using TrapCAD code [40]. The electrons do not take the effect of ions into account in the simulation here though they constitute the cold component of the ECRIS plasma and reduce collectively the total charge to zero. The electrons, in fact, collide with the ions with very high frequency; however, they follow different MLF’s after

each collision. The code gives an idea of the resonance zone, the electron motion, MLF distribution and the magnetic mirror characteristic of a designed minimum-B field. In this exercise, it was found that most of the electrons follow one or the other MLF as anticipated but they are bounced back by the achieved PC-RC mirror field before falling into the loss cone at the chamber surface. One example of the electron simulation is given in Fig. 7 for Ee? and Eek values 10,000 eV and 100 eV, respectively when it is launched at radius 1.0 cm and z = 5.0 cm inside the chamber. The electron continued large number of bounces from the PC and RC positions. The electron continuously drifted along the azimuth due to the curvature of MLF and gradient of the magnetic field. It reached the maximum radius 4.52 cm at z = 0.96 cm with respect to the centre at O(0, 0) after completing almost three rounds. It still continued its journey but was forced to break the motion to preserve the clarity of the simulated electron path for better presentation. Some second order slow drift of plasma particles also takes place towards the higher r and z values because of the interaction of the acquired azimuthal drift velocity with the Bz and Br components of field, respectively. The electron path is depicted in Fig. 7 after three rounds of azimuthal drift approximately about the central z-axis for 28 ls before breaking the electron motion. Similarly, regular mirror reflection and azimuthal drift in electron motion is observed if they are launched at different positions off- axially. But one has to take care of the decreasing mirror ratio as discussed in the following subsection. If the electrons are launched just on the axis, the electrons still show several mirror reflections from the cusp positions PC and RC before being lost. The loss of the slow electrons (of energy < 50 eV) can be either reduced by placing negatively biased disk by electrostatic mirror reflection. The fast electrons can be used to generate secondary low energy electrons by placing thin strips of electron emitting material like aluminum oxide at the cusp positions. Moreover, continuous loss of plasma particles on the entire surface of the plasma chamber takes place in addition to the loss of plasma due to extraction of HCI, which are

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Fig. 7. Electron simulation for 28 ls in the optimized CMF for 18 GHz ECRIS.

compensated by their continuous production at the steady state. A large number of MLF’s, which cross the resonance surface, were also plotted with the help of TrapCAD code. They are depicted in Fig. 8. The colour of the lines MLF changes as it crosses the ECR surface at 6.43 kG field, which is at radius 4.2 cm at the mid-length. It has blue colour at the outside of the ECR surface (higher field region) and yellow colour inside (lower field region). The ECR surface projected in the r–h plane at the mid-length and projected in the r–z meridian plane are depicted in Fig. 8(a) and (b), respectively.1 The extent of the ECR surface in one direction from the centre along the central axis is 3.1 cm. 2.5. Mirror ratio The electrons follow the MLF’s, which form a PC-RC mirror configuration. The calculated mirror ratio, Rm for MLF’s in a quadrant has been plotted in Fig. 9. It is very 1 For interpretation of color in Fig. 8, the reader is referred to the web version of this article.

Fig. 8. The MLF plot to depict the resonance surface corresponding to 6.43 kG field of the shape of oblate spheroid, which is depicted by the position of change of colour of the MLF’s. The figures a and b are the projections in the r–h and r–z planes, respectively.

high in the CMF configuration compared to 2.82 in the old TMF ECRIS of 18 GHz at RIKEN. The MLF’s approaching the plasma centre has higher values pof mirror ratios, so the loss cone angles (aapex = arcsin(1/ Rm)) narrow down also. The electrons get bounced back and crisscross the ECR surface many times to be heated by the microwave to high energy successively. The confinement of these heated electrons is further increased because of the larger perpendicular velocity component (ve?) than the parallel velocity component (vek) with respect to the MLF followed. These electrons come out of the loss cone area in the velocity space because of the anisotropic velocity components. They interact with the atoms and ions and boost the charge state in stepwise manner. Since the confinement of electrons becomes superb, so the confinement of ions too. This process helps to achieve very high density of contained plasma consisting of the HCI’s in the whole large volume of the plasma chamber. It is possible now to extract intense beam of HCI’s of desired species according to the current

M.H. Rashid et al. / Nucl. Instr. and Meth. in Phys. Res. B 262 (2007) 95–104

1000

Along the line equdistant to R and Z

100

Mirror ratio

[2] [3] [4]

10

[5] [6] [7] [8]

[9] [10]

1 0

1

2

3 4 5 6 7 8 Distance from the centre (cm)

9

10

[11] [12]

Fig. 9. Mirror ratio plot on the flux lines passing through points equidistant from radius R at mid-length and central Z-axis. [13]

scaling laws. This may require some ingenious design of the extraction system with the combination of additional small solenoid to reduce adequately the magnetic field at the position of extraction hole and to focus immediately the extracted beam also. 3. Perspective for further improvement The CMF can be used for high or low field corresponding to high or low microwave frequency of the ECR ion source. Plasma confinement can be further boosted by using standard techniques of increasing the magnetic field further at the cusp positions and placing negatively (<1.0 kV) biased disk or cylinder, dielectric material coating [41,42] and metal-dielectric disk at the PC (at the injection end) and metal dielectric ring at the RC on the cylindrical interior surface of the plasma chamber [43]. It can be utilized to generate radioactive ion beam also by putting it in close proximity to the radioactive target because of the fact that it uses no permanent magnet and there is no fear of recurring periodic cost and maintenance due to radiation damage [44,45]. Confinement of plasma is superb for boosting the plasma density to generate HCI and extract intense beam. It can help to achieve the rare beam requirement for advanced particle accelerator. Thus, the CMF ECRIS has bright prospect due to scientific potentiality and technical viability. Acknowledgement The help provided to produce some good quality figures by Lukas Stingelin, a visiting scientist at RIKEN from PSI, Switzerland, is gratefully acknowledged.

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