Tailoring of microwave power density in an ECR ion source using an optimized ridge coupler

One of the interesting areas in the Electron Cyclotron Resonance Ion Source (ECR-IS) design which requires further exploration is the microwave power launching scheme and the power coupling optimization with the plasma chamber. The electron heating efficiency and thereby the plasma density highly depends on the electric field distribution inside the plasma chamber; therefore, it is important to optimize the coupling of microwave power to the plasma chamber, to maximize the electric fields in the plasma chamber for a given microwave power. For this, a single-step quarter wavelength ridge coupler design study has been carried out using CST MW Studio Suite along with the plasma chamber and ridge wave guide designs. The experimental measurements of electric and magnetic field profiles in the plasma chamber assembly with different coupling configurations have been done using an innovative bead pull technique and a magnetic field probe. The experimental results match well with the simulation results and the comparative studies of different coupling configurations reveal that the single step ridge coupler based scheme improves the electric field inside the plasma chamber to at least five times than the conventional ridge waveguide. To further improve the E-field amplitude in the plasma chamber by another 40%, a novel tuning scheme for the coupler has been introduced. Preliminary plasma studies have been carried out with the optimized coupler on a multicusp ECR plasma source and the plasma density measurements performed using a microwave cut-off probe. The plasma measurements show that even at low input microwave powers (∼300 W) the plasma density is comparable with standard ECR-IS. The present study thus, sheds light on the coupling configuration of microwave to plasma chamber with experimental measurements of cavity mode and fields in the cavity which will be useful for high intensity accelerator applications in understanding the plasma evolution, beam parameters and its dependence on different operating parameters.


Introduction
Microwave based Electron Cyclotron Resonance Ion Source (ECR-IS) is widely used in high energy, high intensity accelerators for applications involving radioisotope production, spallation neutron sources, accelerator driven systems, high energy physics etc, since it can produce high intensity and high charge state ion beams with low beam emittance [1][2][3][4][5][6]. A high intensity ECR proton ion source has been developed for the Low Energy High Intensity Proton Accelerator (LEHIPA) at Bhabha Atomic Research Centre (BARC), India [4][5][6]. LEHIPA consists of H+ ion source at 50 keV which is accelerated to 3 MeV by Radio Frequency Quadrupole (RFQ) and thereafter to 20 MeV by an Alvarez type DTL consisting of 4 DTL tanks of 3 m each [7][8][9]. Currently LEHIPA has been commissioned to 11 MeV by acceleration through the RFQ and two DTL tanks [7,8]. The LEHIPA ECR-IS has a two solenoid magnetic mirror field configuration with a conventional four-step ridge waveguide for microwave (MW) power coupling [4,5].
One of the interesting areas of research in the ECR-IS is the MW power launching scheme and the power coupling optimization with the plasma chamber [3,[10][11][12]. The electron heating efficiency and thereby plasma density highly depends on the electric field distribution inside the plasma chamber; therefore, it is important to optimize the coupling of MW power to the plasma chamber, to maximize the electric fields in the plasma chamber for a given MW power [10,11]. This is more important for multicusp based ECR-ISs where the ECR heating efficiency is comparably weaker than the solenoid based ECR-IS [13][14][15][16]. Conventionally in ECR-IS systems, MW power is coupled to the plasma chamber using a ridge waveguide which can enhance the fields near to twice that of plain waveguide coupling [11,12]. There have been efforts to design quarter wavelength coupler for ECR-IS to further improve the power density in the plasma chamber [3]. But, no measurements and analysis of the fields inside the plasma chamber with different coupling schemes have been reported to the best of our knowledge. As part of ongoing research on ECR-IS development at BARC we have developed a test setup for MW power optimization studies of the plasma source. For this, an optimized one-step λ/4 ridge coupler design study has been carried out using CST MW Studio Suite along with the designs of plasma chamber, and ridge wave guide [17]. The simulations show that, with the optimized coupler configuration, the maximum electric field in the plasma chamber has improved considerably to at least five times than with the conventional ridge waveguide coupling scheme. A novel tuning scheme for the ridge coupler has also been studied, which can further improve the E-field in the plasma chamber by another 40%. This tuning scheme is based on a movable tuner in the magnetic field region of the ridge coupler. Based on the simulations, the various components have been fabricated and assembled and electric and magnetic field profile measurements in the plasma chamber assembly with coupler for different coupling schemes have been carried out. Instead of using slotted line-based probes for field measurements in the plasma chamber, an innovative axial bead pull technique has been devised for E field measurements [18][19][20][21]. A magnetic loop probe has been developed for the magnetic field measurements. Preliminary plasma studies were also carried out using this optimized coupler, which was coupled with a multicusp ECR plasma source. The plasma density measurements were carried out using a microwave cut-off probe which measures the electron plasma density using transmission spectrum measurements [22,23]. The design simulations; development of various plasma source components and probes for RF characterization and plasma diagnostics; experimental results of characterization of the field profiles inside the plasma chamber with different coupling schemes, and plasma measurements are presented in this paper.
This article is organized as follows. Section 2 describes the choice of the plasma chamber resonator cavity geometry and the design of single step ridge coupler using CST Microwave studio. The effect of various coupler parameters on electric field distribution of plasma chamber will be discussed here, along with the tuning scheme for E-field enhancement. In section 3 details of the experimental setup and the probes including the magnetic field probe and the bead pull technique which are used for experimental verification of field distribution profiles inside the plasma chamber and coupler are given. Also the experimental setup for the plasma measurements and details of the microwave cut off probe for plasma electron density measurements are also described in this section. The experimental results and analysis are given in section 4 which includes experimental identification of ion source cavity mode, E-field profiles obtained with bead pull technique, comparison of experimental and simulation-based study of different coupling configurations and preliminary plasma studies. Finally, a summary of the main results and conclusions are drawn in section 5.

Simulation studies
In this section, the design simulation studies of the plasma chamber, the 4-step ridge waveguide and quarter wavelength ridge coupler are discussed. These components are part of the experimental test bench for field measurements and plasma studies whose schematic is shown in figure 1. The waveguide adapter, 3-stub tuner, and transition waveguide shown in figure 1 are standard 2.45 GHz microwave transmission line components. The plasma chamber is a cylindrical resonator cavity, whereas the 4-step ridge waveguide and the quarter wavelength ridge coupler are designed in WR 284 rectangular wave guide configuration. The design details of each component are discussed in detail below.

Resonator cavity
Since the microwave power is coupled to the plasma chamber using TE 10 rectangular waveguide mode, TE mode has been chosen to be excited in the cylindrical plasma chamber, with the fundamental resonator cavity mode, TE 111 mode [21,24,25]. The resonant frequency for a TE mode is given by the relation [25], where, r and l are the resonator cavity radius and length respectively, c is the speed of light, r  and μ r are, the relative electrical permittivity and magnetic permeability of the medium filling the cavity respectively and x' mn is the n th zero of the first derivative of the Bessel function of order m. The indexes n, m, p identifies the electromagnetic field pattern of the TE mode. The plasma chamber length, l is typically comparable to the microwave wavelength, λ ∼120 mm, corresponding to 2.45 GHz frequency [12]. Hence, for the TE 111 resonant cavity mode operating at the microwave frequency of 2.45 GHz, the plasma chamber dimensions are chosen to be r = 42.5 mm and l = 113 mm, using equation (1).
Eigen mode solver of the CST MW Studio has been used to identify the Eigen modes of the resonator cavity which are allowed by the boundary condition i.e. E t = 0. Figure 2 shows the CST plot of electric and magnetic field distributions in the cylindrical cavity resonating in TE 111 mode at 2.45 GHz. Introducing an opening to the resonator cavity for MW power coupling as shown in figure 1, causes a small shift in the resonant frequency and new Eigen modes allowed by the boundary conditions can also come into picture. This shift in resonance frequency has been taken care by slight adjustment of the length of the resonant cavity.

Coupler design 2.2.1. 4-step ridge waveguide
In conventional ECR based ion sources, a 4-step ridge waveguide is used to couple the MW power to the plasma chamber [3,11,12]. The S 11 parameter plot of the WR284, 4-step ridge waveguide designed for the 2.45 GHz plasma chamber is shown in figure 3. The reflection coefficient, S 11 is below the −30 dB level, for the bandwidth of 2.45 GHz ± 25 MHz of the microwave generator.
Frequency domain solver in CST MW studio has been used to simulate the Electric field profile in the plasma chamber and 4-step ridge wave guide assembly. The contour plot of E-field distribution in the assembly is shown in figure 4(a) and the on-axis E-field amplitude plot of the configuration is shown in figure 4(b). Figure 4(b) shows that the ridge waveguide increases the E-field at the centre of the plasma chamber (z = l/ 2 = 56 mm) as compared to the E-field amplitude in the ridge waveguide section.

Quarter wavelength ridge coupler
To further enhance the E-fields inside the plasma chamber, a single step ridge coupler with λ/4 length has been designed, in addition to the ridge waveguide. In the design of the power coupler, special attention needs to be given to the electric field amplitude in the plasma chamber since power transferred to the plasma is proportional    to the electric field distribution in the plasma chamber and hence by increasing the field strength, plasma density can be amplified for the same input microwave power [3].
The 3D model of the ridge coupler with the optimization parameters is shown in figure 5. The waveguide dimensions correspond to WR 284 (length, L = 72 mm and width, W = 32 mm) and the ridge thickness, t has been taken to be ∼λ/4. The other coupler parameters like ridge width, S, ridge gap, h etc were optimized in design simulations to maximize the TE 111 mode electric field distribution at the centre of cylindrical plasma chamber.
The simulation results of the optimization process of two important coupler parameters are shown in figure 6. The frequency domain solver of CST MW studio is used for the simulations. The assembly configuration used in these simulations is as follows. The cylindrical plasma chamber of length 113 mm, followed by the single step ridge coupler and there after the 4-step ridge wave guide. Figure 6(a) shows the variation of electric field distribution with different ridge gap, H along the assembly axis, z and figure 6(b) shows the effect of ridge width, S on the axial electric field distribution.
Based on the coupler parameter optimization to maximize the electric field amplitude in the plasma chamber, the optimal coupler parameters obtained are; coupler length, t = 30 mm, ridge width, S = 18.5 mm, ridge gap, h = 4.6 mm. With the optimized coupler parameters, the electric field amplitude in the centre of the plasma chamber (z = l/2 = 56 mm) is eight times more than that in the ridge wave guide section. The electric  field amplitude in the single step ridge coupler is also high due to the small ridge gap, which means that proper cooling solution might be provided for the coupler operation in CW mode. A comparison of the power coupling configurations, with and without the single step coupler is shown in figure 7, where the single step coupler design and the conventional design with ridge wave guide are compared. With this optimized coupler configuration, the maximum electric field in the plasma chamber has improved considerably to around five times than with the conventional ridge waveguide design. Figure 8 shows the CST MW studio contour plot of the electric field distribution in the assembly with the optimized coupler design. In order to further improve the electric field amplitudes in the plasma chamber, a tuning scheme has been proposed for the ridge coupler. Since the ridge coupler is a quarter wave length structure, it acts like a resonant cavity in itself, with well-defined locations of electric and magnetic fields. For the field tuning, a cylindrical tuner has been inserted in the magnetic field region of the one step ridge coupler at a distance of 0.5 mm from the plasma chamber. Effect of tuner depth and diameter on the electric field amplitudes have been studied using the CST simulations. For the tuner depth analysis, the tuner diameter was fixed at 6 mm. It is found that electric field amplitude at the centre of the plasma chamber increases linearly up to a certain tuner depth and then decreases sharply as shown in figure 9 (a). Around 20% improvement is E-field amplitude was observed with a tuner depth of ∼3.5 mm as compared to the ridge coupler design without tuner. Slight variation of ∼1 MHz was observed in the resonant frequency of the plasma chamber assembly due to the inductive effect of tuner in the magnetic field region.
A further optimization study was conducted with respect to the tuner diameter. The tuner depth was fixed at 3.25 mm for this study. A further increase in the field amplitude to about 17% was observed in this case, with the  E-field amplitude increases almost linearly with tuner radius, peaks around 5 mm tuner radius and then decreases. The overall improvement in E-field amplitude is 40% more than the case without the tuner. Since the ridge coupler couples the MW power in the magnetic field region of the plasma chamber, the tuning in the magnetic region of the coupler proves effective.
As the fabrication and assembly errors can lead to field deterioration in the plasma chamber assembly, the proposed E-field tuning scheme using the movable tuner will be useful. The tuner effect was also studied in the electric field region of the ridge coupler where the E-field enhancement was not observed, whereas frequency variation was more prominent due to the capacitive effect.

Experimental setup
Since plasma formation and electron heating depends on the MW electric and magnetic profiles in the resonator cavity, the experimental validation of the simulation results is important. Based on the design studies described in section 2, the different components of the plasma chamber assembly including the plasma chamber, quarter wavelength ridge coupler and the 4 step ridge wave guide have been fabricated and assembled on a test bench to characterize the resonator cavity and coupler, as shown in figure 10. The tuning scheme of the coupler using movable tuner is not used in the present experiments.
As shown in figure 10, the test bench assembly for low power MW measurements also includes a 3-stub tuner and a WR340 to N type adapter; apart from the plasma chamber assembly. A vector network analyser, (VNA, Rohde & Schwarz ZVL6) connected to the N type adaptor has been used for the field measurements. The two different measurement techniques that have been used for cavity characterization are described below.

Magnetic field probe
A magnetic field probe was used for the identification of the required resonant cavity mode at ∼2.45 GHz, from the wide spectrum of cavity modes. The single loop magnetic field probe shown in the inset of figure 10 has been used for these measurements. This magnetic loop was inserted along the axial end port of the plasma chamber and moved along the chamber axis using a motorized 3 axis stage as shown in figure 10. The voltage induced due to time varying magnetic field at each probe location was measured with the help of an oscilloscope and normalized magnetic field profile was plotted along the chamber axis.

Bead-pull technique
In order to measure the electric field profile in the plasma chamber, bead pull technique has been used which is based on the well-known Slater small signal perturbation theory which provides the basis for measurements of Electric and Magnetic field configuration inside resonant cavities [20,21]. If a small bead of any shape is inserted into the cavity, the perturbation introduces a shift in the resonant frequency. For a spherical bead of volume V , D the shift in resonant frequency, Δω o is given as a function of the unperturbed electric (E) and magnetic (H) field amplitudes, with the assumption that field is constant over the bead, where r e and r m are the relative permittivity and permeability of the perturbing material and U is the total stored energy which is the sum of E and H field energies. For a spherical dielectric bead with r m = 1, the frequency shift is given by Conventionally, in the bead pull measurements, the bead on a Nylon string is pulled axially through the resonant cavity using a motor and pulley guide mechanism [20]. In the case of the plasma chamber assembly this method is not possible since the MW power is coupled axially using the waveguide and the pulley guide mechanism cannot be used. Hence an innovative technique has been devised for the bead pull measurements in the plasma chamber, where a Stainless Steel (SS) wire with bead mounted on one end was introduced axially in the plasma chamber as shown in figure 10. A stepper motor controlled XYZ stage was used for the precise alignment of the bead-on-wire assembly and for the bead pulling measurements. The perturbation at any bead position causes a frequency shift of the cavity mode, as observed in S 11 measurements using VNA, which is proportional to the square of the local E field configuration. Once the bead-pull data with the bead-on-wire configuration was taken, the data with only wire is taken to isolate the contribution of the bead.

Plasma measurements
A 2.45 GHz multicusp ECR plasma source has used for the plasma studies with the optimized coupler configuration. The experimental set-up used for the plasma measurements is shown in figure 11. The continuous mode microwaves from the microwave generator (Sairem GMP20KIP, 2 kW) are guided to the plasma chamber via standard WR340/284 waveguide components, the ridge waveguide and the ridge coupler. The same plasma chamber developed for the coupler studies has been used here.
A 14-pole permanent magnet multicusp geometry is used to generate ECR zone inside the plasma chamber along with plasma confinement using the minimum B-field configuration [13,26,27]. The ECR zone corresponding to the MW frequency of 2.45 GHz exists along an annular region within the plasma chamber at ∼3.75 mm radius as shown in figure 12. Argon plasma was used for the preliminary studies.
A microwave cut-off probe which is shown in the inset of figure 11 has been developed for the measurements of plasma frequency and thereby plasma electron density. This microwave probe gives a quick information of the plasma frequency by use of the transmission spectrum measurements with a VNA [22,23]. The microwave cut- off probe consists of dual antenna tips which are part of 50-ohm coaxial RF cables. The dual antenna of the probe, which is exposed to plasma, is about 10 mm long and has a separation of about 3 mm. The transmission spectrum (S 21 ) from the probe is measured by using a vector network analyser. The radiating antenna of the probe is used to generate the electromagnetic wave signal in the plasma and the propagating signal is detected by the receiving antenna.
Dispersion relation of an electromagnetic wave propagating through a non-magnetized plasma or for an ordinary wave in a magnetized plasma is given by [23,28].
where w is the electro-magnetic wave frequency, k is the wave number and p w is the electron plasma frequency which is given by the relation, where n e and m e are the electron plasma density and electron mass respectively. MW frequencies lower than the plasma frequency, p w are attenuated in the plasma medium, while the higher frequencies propagate through the plasma. Hence, in the transmission spectrum (S 21 ) using the wave cut-off probe, a distinct minimum peak which corresponds to the plasma frequency or the cutoff frequency, can be observed and by using equation (5), the plasma electron density can be calculated.

Resonant cavity mode identification
As mentioned in section 2, with the optimized coupler configuration, the first experimental step was the identification of the required cavity mode at ∼2.45 GHz, which is the dominant cavity mode (TE 111 ). The S 11 measurements were made in the plasma chamber assembly shown in figure 10 and the measurements showed a cavity mode at 2.4488 GHz which has been tuned using the 3-stub tuner to minimize the return losses. As shown in figure 13, the measured S 11 plot of this cavity mode with return losses < −35 dB, indicates very good MW power coupling with the plasma chamber. The shift in frequency of −1.2 MHz is due to the incorporation of the waveguide transmission line with the plasma chamber. An ambient temperature dependence of the resonant frequency was also observed which is of the order of few kHz.
In order to verify whether this cavity mode is the required TE 111 mode or not, the magnetic field probe was used. Figure 14 shows a comparison between simulated and experimentally measured normalized magnetic field profile along the plasma chamber axis using the probe. The close agreement of the measured magnetic field profile with the simulated one provides clear evidence of the mode present in the plasma cavity to be TE 111 mode. Magnetic field profile contour plot for the resonator cavity along with the waveguide line is shown in figure 15 which also shows the magnetic field coupling with the plasma chamber.

Bead-pull measurements
Once the ion source cavity mode was identified, next step is to measure the electric field profiles inside the plasma chamber. For this, on axis bead-pull measurements have been done inside the cavity and the ridge coupler extending into the ridge waveguide. A 4.8 mm long and 4 mm diameter Teflon bead was used in the measurements, which was moved on a 1 mm diameter SS wire using motorized 3 axis stage in steps of 1 mm. To compare the experimental data with the simulations, a bead pull simulation has also been performed in CST MW Studio keeping the same bead parameters as in the experiment. In figure 16 the experimentally obtained frequency shifts has been compared with the frequency shifts from CST simulation.
From figure 16, it can be seen that the experimentally observed frequency shifts are very close to the simulated frequency shifts. Slight discrepancy is observed in the in the coupler region which can understood from the fact that the ridge coupler is a quarter wavelength structure with well-defined regions of E field and B field. The bead which has a comparable size as the coupler gap, when enters the high E field region of the coupler can cause larger perturbation of the fields due to the capacitive effect and this reflects in the frequency variation. Bead alignment errors due to wire sagging effect may get amplified as well.
To calculate the electric field amplitude from frequency, shift data given in figure17, the form factor for the dielectric bead need to be calculated (cf equation (3)). For a cylindrical dielectric bead there is no well-defined relation for form factor calculation; however, an approximation for the form factor can be used [20]. The comparison of the on axis experimental electric field data with simulated electric field is given in figure 17.
Two regions of interest are there in figure 17; (I) plasma chamber and (II) one step ridge coupler. Figure 17 shows that the experimental electric(E) field profile is in a close agreement with the simulated profile, especially in zone (I).
For better understanding the coupler performance, another coupling configuration was also studied. Here, the 4 step ridge waveguide after the ridge coupler has been replaced with a WR 284 plane waveguide. To validate  the measurements, a comparative study of both configurations has also been done in CST MW Studio as shown in figure 18. It can be assumed that the presence of the ridge wave guide will have a positive effect in the field amplitudes in the plasma chamber due to the presence of the ridge section which can lead to better impedance matching. But in the simulations, similar electric field amplitudes have been observed for both the configurations, as shown in figure 18. To validate these simulation results the bead pull measurements for the plasma chamber region has been carried out and the comparison of the frequency shifts for both the configurations is shown in figure 19.
Both simulation and experimental results shows that there is no extra advantage with the ridge wave guide configuration. Even with the plane wave guide configuration, similar electric field amplitude levels can be obtained in the plasma chamber with the optimized single step ridge coupler as evident from figures 18 and 19. This unique behaviour observed with the quarter wavelength ridge coupler provides us the freedom to use any waveguide configuration for plasma ignition and hence can have shorter MW transmission lines for ion sources.

Plasma studies
Preliminary plasma studies using the optimized ridge coupler configuration is discussed here. A microwave cutoff probe which for plasma diagnostics is inserted along the axial port of the plasma chamber with the dual antenna portion of the probe, exposed to the plasma. The radiating antenna of the probe generates the electromagnetic wave signal in the plasma, using a Vector network Analyser (VNA) and the propagating signal is detected by the receiving antenna. Figure 20 shows the transmission wave spectrum (S 21 ) with plasma on and off conditions. With the plasma off condition, the peaks observed in the transmission spectrum corresponds to the cavity modes. With plasma on, a distinctive dip is observed in the transmission spectrum at lower frequency of ∼1 GHz, which corresponds to the electron plasma frequency and by using equation (5), the electron plasma density is calculated.
The variation in electron plasma density of the plasma source with input microwave power is shown in figure 21. The optimized operating gas pressure during this experiment is 2.4 mTorr. The wave cut-off probe results show that, even at low input MW powers the plasma density is comparable with the LEHIPA ECR-IS  which operates at > 1 kW MW power [29]. This clearly points at the better coupling of MW to the plasma chamber with optimized one step ridge coupler.

Summary and discussion
In summary, the detailed study of the design, development and characterization of a microwave plasma chamber assembly with a one-step ridge coupler has been carried out. The one-step quarter wavelength ridge coupler geometry has been optimized with CST microwave studio for the enhancement of electric field amplitude at the centre of the plasma chamber. In the present study the ridge width of 18.5 mm and ridge gap of 4.6 mm for λ/4 ridge coupler is found to be optimal for the improving the electric field amplitude to atleast five times as compared to the conventional ridge waveguide configuration. Also, a novel tuning scheme has also been proposed for the ridge coupler which can further improve the E-field in the plasma chamber by another 40%. Different measurement techniques have been used to characterize the ridge coupler configuration. The presence of TE 111 cavity mode is identified experimentally with the help of S11 measurements. A magnetic field probe and an innovative bead-pull setup were used for the B field and E field measurements in the plasma chamber. Magnetic field probe results match well with the CST simulation results. The bead-pull measurement results show that the electric field gets enhanced in the plasma chamber due to the ridge coupler as predicted by the simulations and the measurement and simulation results are in good agreement. This will be useful in increasing the plasma density for a given microwave power. The plasma studies using a microwave cut-off probe show that plasma electron densities are comparable to standard ECR-IS and is attained at low MW powers. This work, thus provides insight into the importance of power optimization based on the coupling studies of microwave to the plasma chamber with the help of an optimized coupler design, which will be useful for the development of a high intensity ion sources for high intensity accelerator applications.