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Comments to date: 3. Page 1 of 1. Average Rating:
d 10:40am on Wednesday, August 11th, 2010 
Overpriced content consumption table. Very responsive touch screen, high res screen Content Consumption only. Not great value for money. No camera.
JacksonLongstreet 5:17am on Friday, July 16th, 2010 
PROS: OS, look, Awesomeness ITs great, and the idea is well along with the OS its a Mac downsized. its size is a bit big Bought the 16G WiFi for my wife. She enjoys playing games, surfing the web, reading books, reading email and catching up on her Soaps at Awesome game player, and has replaced my laptop but I do not have to need for business and so I do not know about how those work. Great for traveling,...
sYph0n 8:34pm on Saturday, May 1st, 2010 
Love both the silicone case and zebra sleeve pouch. This product is EXACTLY what I wanted. It fits perfectly and it got here very fast. The item was all that the description said it would be! I am very pleased with this product and would recommend it to friends.

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A Study on the Ion Beam Control of Cyclotron using Intelligent Control
Yu-Seok Kim Young-Ho Cho Jong-Seo Chai Key-Ho Kwon
Abstract - Recently, as the field of cyclotron application is to be wider, to inject the beam where the user want to is getting more important. But since it is not the easy way to describe the model equation of cyclotron, it could be operated by only operator's experiences. In this paper, we suggest the cyclotron controller using the fuzzy logic and the genetic algorithm. The proposed controller was verified in useful by applying to the cyclotron's beam line. In the experiment the measured results were obtained by VXIbus and the control algorithm was performed by LabWindows/CVI. Key Words : Cyclotron, Fuzzy Controller, Genetic Algorithm, VXIBus, LabWindows/CVI


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[1] R. Westervelt, W. Klein, "Framework for a General Purpose, Intelligent Control System for Particle Accelerators", Proceeding of the Particle Accelerator Conference and International Conference on High Energy Accelerators, IEEE, pp.2175-2177, May, 1995. [2] J. S. CHA1, Y. S. KIM AND K. H. KWON, "Beam Transport System using Fuzzy Controller in the KCCH Cyclotron", Cyclotrons and Their Applications, Proceedings of the 14th International Conference, pp.310-313, 1996. [3] S. Clearwater and W. Cleland, "A Real-Time Expert System for Trigger Logic- Logic Monitoring", Proceedings of International Conference on
Accelerator and Large Experimental Physics Control System, November, 1989. [4] D. Nguyen and M. Lee, "Accelerator and Feedback Control Simulation Using Neural Networks", SLAC-PUB-5503, May, 1991. [5] D. Schultz, "The Development of an Expert System to Tune a Beam Line ", Proceedings of International Conference on Accelerator and Large Experimental Physics Control System, November, 1989. [6] S. Kundu and J. Chen, "Design of Heuristic Fuzzy Controller", Fifth IEEE Int. Conf. on Fuzzy Systems, pp.2130-2134, 1996. [7] H. Ishibuchi, K. nozaki and H. Tanaka, "Efficient fuzzy partition of pattern space for classication problem," Fuzzy sets and Systems, vol. 59, pp.295-304, 1993. [8] E. H. Mamadani, "Application of fuzzy logic to approximate reasoning using linguistic synthesis", IEEE Trans. Computer, Vol.C-26, nol2, pp.1182-1191, 1977. [9] L. Chambers, Practical Handbook of Genetic Algorithms, Applications Volume I, CRC Press, 1995. [10] K. Kristinsson and G. Dumont, "System identification and control using genetic algorithm", IEEE Trans. System, Man, Cybernetics, vol 22, no. 5, pp.1033-1046, 1992. [11] J. R. Koza, Genetic programming, MIT press, 1993. [12] Robot T. Cleary, "A New CAMAC and VXIBus High Performance High Performance Highway Interconnect", IEEE Transation on Nuclear Science, Vol. 44, No. 3, pp.393-397, June, 1997. [13] E. J. Barsotti, "The new VME64 Extensions Standard, Related VSO and IEEE Standards & VME International Physics Associatdon(VIPA) Activities", Nuclear Science Symposium, Anaheim, CA, Nov. 3, 1996. [14] W. R. Hwang and W. E. Thompson, "Design of intellegent fuzzy logic controllers using genetic algorithms", Proc. of Third EEEE int. conf. on Fuzzy systems, pp. 1383-1388, 1994. [15] *W*\, 7d-fr*} "MC-l l - a S. <", KAERI/MR-298/97, pp. 77-79, 3fl-7l#^, 1997. [16] 3-fH!, 1$H, *m*\, ^ 7 l s "VXI A l ^ - i pp979-984, 1998. [17] LabWindows/CVI, National Instruments Corporation, 1996.

Beam Emittance Measurements Using Alumina Screen at KCCH-MC50 Cyclotron
Shin-ichi Watanabe Center for Nuclear Study, Graduate School of Science, University of Tokyo 3-2-1, Tanashi-shi, Midori-cho, Tokyo 188-0002, Japan Jang-Ho Ha, Yu-Seok Em, Hye-Young Lee and Jong-Seo Chai Cyclotron Application Laboratory, Korea Cancer Center Hospital Gongneung-Dong, Nowon-Ku, Seoul, Korea
Abstract The transverse beam emittance of the medical cyclotron KCCH-MC50 in Seoul was determined from measurements of the beam width on a profile monitor as an upstream quadrupole field is varied. The beam profile monitor system comprises the 99.5 % alumina with chromium oxide, an industrial TV camera, and an image data stored system. Using the stored data on the personal computer makes detailed analysis of the beam profile. The measured beam emittance derived from FWHM of the beam profile is a good agreement to the designed factory data. In this presentation, we describe the experimental setup, results, and conclusion of beam emittance.

1. Introduction

A transverse-beam emittance can be measured using the lattice optics of a transport line and a profile monitor located where the betatron sizes of the beam dominate. In an example of the quadrupole - drift - profile monitor method, a quadratic dependence of the beam width is given by Y=A(k-B)2+ C (1)
Here Fis the square of beam width and kis B'L/Bp of an upstream quadrupole magnet. The coefficients of A, B, and Care obtained from the quadratic curve fit parameters.
The beam emittance i?is given by
where the factor L is distance between a center of quadrupole magnet and the fluorescence screen. Various kinds of beam emittance monitor, which is based on the quadratic dependence of the beam width, have been developed for the electron machine. [1,2, and 3] These monitors feature the measurement of small emittance beam. The width of electron beam is sensitive to the strength of upstream quadrupole magnet (lvalue control) because the electron mass is small compared with ions at the identical magnetic rigidity. This method is seemed to easy to measure the beam emittance of the electron beam because an electron gun provides unified beam structure like the single spot beam source. On the other hand, this method is seemed to difficult to measure the beam emittance of the multi-charged ion source because of complicated beam structure. Is it applicable to the large emittance beam such as the beam from the ECR ion source or the cyclotron ? The INS, University of Tokyo, had been tested the alumina screen using the 26 MeV Alpha beam [4] because the hardness and chemical property against the irradiated nuclear beam full fill the operating condition. The alumina screen, which is the one of the fluorescence screens, has still major contribution to diagnose a density, width, and center of the nuclear beam at the still low beam current below 10 pA. The Kyoto group developed the beam emittance monitor for the proton beam, where was measured by using the alumina screen at the kinetic energy of 50 KeV, 1 MeV, and 7 MeV [5]. The CNS-KCCH group has been promoting the development of the beam emittance monitor using the alumina screen, which had originally been proposed as the 2nd step of the monitor development following achievement of preliminary test at the sector focussing cyclotron (K=68) of Center for Nuclear Study, University of Tokyo. The measurement of beam emittance using the alumina screen was performed at the medical cyclotron KCCH-MC50 in Seoul (K=50). To measure the beam emittance, CNS group had provided the alumina screen, data acquisition board, and data acquisition software. In this presentation, we describe the beam profile monitor using the alumina screen, beam experiment, data analysis of measured profiles, calculation of beam optics, and the conclusion of beam emittance. Main contribution to the beam profile is an uncertainty of the ion source. The lack of uniformity and the incomprehensible behavior of the ion source are excluded in this presentation.

The beam profile data saved on the hard disc were analyzed by using the imageprocessing tool in order to measure the beam sizes on the alumina screen. A difficulty of the image data processing is mathematical processing such as a subtraction of noise signal from the measured beam profile data. The brightness and quality of the measured beam profile are influenced by the noise signal, unavoidable beam hallo, and time structure from the ion source. The image-data processing tool offers the function to show the three dimensional (3D) data in X, Y, and Z coordinates. Fig. 6 shows the 3D display of the beam profile data as shown in Fig. 5-1. The axis X and Z shown in Fig. 6 represent the twodimensional coordinates associate with a surface of the alumina screen plate. The axis Y represents the beam intensity. In Fig. 6, the top of contour map is recognized as a center of beam profile irradiated on the alumina screen. The tail noise in the beam profile is taken into account the systematic error of the associate beam width. The pixel number in the beam profile data gives the beam intensity irradiated on the alumina screen. For example, Fig. 7 shows that the X and Y-axis represent the pixel number and the beam intensity, respectively. On the other word, the X-axis represents a radial direction of the transported beam. A spectrum height, which is the beam intensity, is a projection of the pixel data along the Z-axis. We can calculate the beam size by using the digital scale function supported by the imageprocessing tool. The tail noise and a fluctuation of the spectrum are to be subtracted from the original data when a calculation of the beam emittance. Various definitions of the beam width are in use to calculate the beam emittance. We discuss here the Gaussian distribution associate with the beam width of the standard deviation a. The full width at half maximum (FWHM) and the full width at 90 % maximum are discussed in the following section.

4. Discussions

4-1 Beam condition The beam emittance measurement has been done under the following boundary conditions; the fluorescence due to the irradiation of the nuclear beam is proportional to the beam current; the light intensity of the fluorescence is not decreased by experiences of the medium between the alumina screen and the focussing point of the ITV camera; the dynamic range of the sensitivity to the light flux is infinitive. A saturation level of the alumina screen is considered to evaluate the dynamic range of the alumina screen to the irradiation level of the nuclear beam. A linearity of the fluorescent flux to the irradiated beam current is estimated. An estimated beam
current excess 250 nA/cnr irradiated to the alumina screen deteriorate a linearity of fluorescent flux. This estimation is derived from the preliminary test using a 26 MeV Alpha beam from the sector focussing cyclotron of Institute for Nuclear Study, University of Tokyo [4]. The beam current of 1.5 nA was chosen at the experiment using the KCCH-MC50 cyclotron. We assumed that the beam density is flat in the irradiate area and the beam current is constant during the beam profile measurement. Thus, the estimated beam intensity is 47.8xlO7 e/mm2 s as the beam current is 1.5 nA. A recommended lifetime, which is an integrated beam intensity to the unit area, of the alumina screen is lxlO18 e/mm2. The estimated beam density is 2.5xlO7 e/mm2 s at the beam sizes of 25 x 15 mm2 on the associate alumina screen. A threshold level from the view point of the excitation of the fluorescence is lxl07e/mm2 s. So the beam sizes above mentioned are acceptable area at the beam current of 1.5 nA. If the lack of data due to a timing coincidence is existed in the measurement system, signal conditioning circuit is to be used in the experimental setup. We have had considered the synchronization of the beam profile to the image data processing circuit. The cyclotron beam gives bunching structure due to the given energy from the Dee of the cyclotron. A decay time of the fluorescence emitted from the alumina screen is estimated at 3 x 10'3 sec. We could say that the time periods of the cyclotron bunched beam is faster than this decay time. This means that the lack of beam profile data is not occurred during the irradiation of the beam on the alumina screen. 4-2 Beam optics and beam width To estimate the beam width, using the computer has done the beam transport simulation [6]. In the calculation, the twiss parameter at the exit of KCCH-MC50 is assumed that (3x=1.534 m, (3z=3.303 m, ax=0.2138, and ccz=0.6883, where is derived from the designed factory data of KCCH-MC50. The designed factory data is 4.2 mm, 2.8 mrad, and 11.5 rc-mm mrad for X, X\ and Ex, respectively. The designed factory data is also 6.8 mm, 2.5 mrad, and 14 7t-mm mrad for Z, Z\ and Ez, respectively. For convenient, dispersions nx=0.73 m and r\z~0 m, r\xr-0 and T|z'=0, where is the reference of K68-SF cyclotron at CNS, U-Tokyo, is taken into account the estimation of the beam envelopes. Using these parameters, the beam width at the alumina screen has been calculated as the upstream QU8 current is varied. The calculated beam envelopes are shown in Fig. 8. The beta functions and dispersion functions (twiss parameter) of the beam transport line are shown in Fig. 9. Figs. 8 and 9 show the example of the beam optics in case of the upstream current QU8 current is 18.1 A. The k-value dependence of the measured beam width, which is full width at 90 %

5. Summary

The quadratic dependence of the beam width was measured at the KCCH-MC50 cyclotron. The summary is as follows: We show the beam profile data measured with the alumina screen, Al2O3+CrC>3 plate of AF995R (Desmarquest) with 1-mm thickness. The extracted beam current is 1.5 nA protons at 50.5 MeV. The beam profile was measured with ITV camera system and was analyzed with the image processing tool. The beam profile data was evaluated to determine the transverse beam emittance according with both the projections where the full width at 90 % maximum and the FWHM. The measured beam emittance based on the beam width of FWHM is a good agreement to the designed factory data of Ex = 11.5 and Ez = 14 7r-mm mrad, respectively. 6. Acknowledgments The authors wish to thank the cyclotron crew of the KCCH-MC50 cyclotron application laboratory for their helpful operation. The first author thanks Prof. Y.Shida for his valuable comments and discussions. This work was supported in part by grant-in-aid for Joint Research Project under The Japan-Korea Basic Scientific Promotion Program (KOSEF-JSPS).


[1] M. C. Loss et al., "Automated Emittance Measurements In The SLC",SLAC-PUB4278, March 1987 (A) [2] M. C. Loss etal, "High Resolution Beam Profile Monitors In The SLC", Transaction of Nuclear Science, Vol.NS-32, No.5, Oct. 1985. [3] Y. Hashimoto et al.,"Beam Profile Monitor Using Alumina Screen And CCD Camera" INS-T-511, Aug. 1992. [4] S. Watanabe et al. "Beam-Profile Measurement with an Al2C>3+Cr Plate", Annual Report 1994, INS Tokyo-University, pp25-26. [5] T. Shirai et al., "Emittance Monitor With View Screen And Slits", Proc. of Linac'94, Japan, 1994. [6] Phil Bryant, CERN, private communication,
Table 1. The Characteristics and Specifications of MC 50 Cyclotron


Accelerating particles
Energy 20 ~ 50 MeV - MeV 25 ~ 52 MeV 20 ~ 70 MeV
Beam intensity 60 p A 30 p A 30 p A 20 p A

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143 cm 11 cm 19.7 cm

. max. pairs 17.5 kG 10.5 kG 20.5 kg 1 X 10

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Table 4. K-value dependence of the measured beam width ( FWHM)
K m 4.931 5.117 5.178 5.238 5.3 5.42 5.54 5.602 5.663 5.72 5.84 5.965 6.025 6.328 6.449

The 4th Korea- Taoan Toint Symposium on Cyclotrons and Nuclear Science.
Compact cyclotrons for medical application Hajime Saito Quantum Equipment Business Center, Sumitomo Heavy Industries, Ltd. 9-11 Kitashinagawa 5- chome, Shinagawa-ku, Tokyo, 141-8686, Japan
Abstract Sumitomo Heavy Industries(SHI) has been active in the field of particle acceleration since 1970, and delivered an extensive series of accelerator systems of electrons and ions of energies ranging from a few hundred keV to several hundred MeV. Recently, Compact AVF cyclotrons have been developed and are added in the product line for the application in the medical field. Negative-ion cyclotrons named HM-18 and HM-12 are for production of radio isotopes, Carbon-11, Nitrogen-13, Oxygen-15 and Fluorine-18 to be used in Positron Emission Tomography (PET). HM-18 produces 18MeV protons and lOMeV deuterons , and HM-12 does 12MeV protons and 6MeV deuterons. Fixed energy proton cyclotron C-235 is for cancer treatment, supplies 235MeV protons in the beam current over 500nA, and has been developed under the joint cooperation with Ion Beam Application (IBA), Belgium. The design concept and running performance of these machines will be presented.
The 4th Korea- laoan foint Symposium on Cyclotrons and Nuclear Science
Design of RF System for a new PET Cyclotron Jang Ho HA
Korea Cancer Center Hospital, Korea Atomic Energy Rearch Institute, Seoul, Korea e-mail:
Abstract We design the RF resonator system for a new PET cyclotron dedicated PET tracer isotope production. The dimension of RF cavity and dee is determined by the effective j wave method with the zero-impedance at a 72 MHz frequency. The cavity design is specified that the R.F. is 72 MHz, the power is 10 kW, dee voltage is 40 kV, dee angle is 43.6, dee length is 50 cm. We designed the resonator with consideration of the dee-liner distance and co-axial cavity length. The dee designed by perfoming three type of system calculation that they shows different capacitance between dee and liner. The coupling mode is inducetive coupling. The test bench of RF system was installed and will test.
The 4th Korea- Japan Joint Symposium on Cyclotrons and Nuclear Science
Upgrading of Cyclotron Control System S. WATANABE, Y. OHSIRO, N.YAMAZAKI, H.MUTO, S.KUBONO, Y. SHIDA, T.KATAYAMA, and M.SEKIGUCHI Center for Nuclear Study, Graduate School of science, The University of Tokyo, Midoricho 3-2-l,Tanashi, Tokyo 188-0002, Japan
Abstract The most the existing cyclotron facilities are constructed for the nuclear experiments, medical applications, and industrial applications. Especially, advanced cyclotron facility covers either the many application fields or the dedicated field such as the medical application. Prom my view point, meaning of advanced cyclotron facility provides the features relevant to high quality beam, variety of ion species, and high current beam sources. The coupled works relating with accelerator science and beam technology are main part of the upgrading of cyclotron facilities. For examples, Cyclotron with K-number of 68 at CNS (Center for Nuclear Study, The University of Tokyo) is devoted for improving the ion source, external injection system, rf system, control system, and beam diagnostic system. These works excepts the ion source have been done from the following point of view; improvement of beam optics of external injection system aiming at highest transmission efficiency; improvement of operating performance of present cyclotron assisted by advanced computer technology; and development of beam diagnostic system based on the advanced accelerator technology. The computer control system is a framework of the advanced cyclotron facility and their relative importance is increased in accordance with a variety of cyclotron facilities. The most advanced computer technology such as WWW enable us seamless cyclotron control with the aid of multimedia technology. The data logging, image data processing, and beam diagnostic system have been developed to study the newest cyclotron control system. The developed system enable us browsing the operation status of CNS cyclotron by using the personal computer linked with local area network. The developed system is applicable to radiation safety control because of distributed radiation detector and safety check system. The present paper discusses the applied WWW technology relating with CNS cyclotron facility. The paper also discusses the study of beam diagnostic and control relevant to the improvement of external injection system.

The 4th Korea- loom Joint Symposium on Cyclotrons and Nuclear Science
The design of the PIG ion source for the negative hydrogen.
Hyeyoung Lee1, S.A.Shin1, S.Oh2, M.Yoon2, J.S.Chai 3 , J.H.Ha 3 1) Department of Physics, Ewha W.Univ.,Seoul 2) Department of Physics, POSTECH S) Cyclotron Application Lab.,KCCH-KAERI
Abstract A Penning Ionization Gauge (PIG) ion source is constructed to produce an intense H~ beam. The purpose of our investigation with this source is to develop an H~ PIG source with a significantly smaller dimension in geometry so that the final version of this source will be comfortably placed in the central region of the PET cyclotron which is under construction. This reduction in dimension is expected to improve the overall performance of the PET cyclotron. As the cathode material we use LaB6- The ion source is placed at the center of non-magnetic stainless steel vacuum chamber with an inner radius of 140 mm and then the chamber itself is inserted in the space between the top and bottom magnet pole. For a visual investigation of the source performance, the chamber has two see-through windows. Attainable vacuum pressure, when the gas is turned off, is 5xlO~6torr. The magnetic field is simulated using the POISSON-2D and then TOSCA-3D. The excitation coil is of a borrow copper conductor type, the dimension of which is determined after the consideration of generation and the pressure drop of the cooling water. H~beam has been observed with an arc power of 2kV,lA. The extraction voltage is positive 17kV. Theoretical calculations for the trajectories of ions from the anode slit to one extractor electrode are carried out to find the optimum position and width of the extractor slit. They indicate that the slit has to be at least 2.0mm wide with its center shifted towards the Faraday cup by 1.0mm. A Faraday cup is constructed and installed inside the chamber. The cup can be biased to positive 50V to prevent secondary electrons from escaping. After solving the initial problems of high voltage breakdowns and sparking in the cathode-anode region of the source, we finally succeed in collecting the negative ions in the Faraday cup.
The 4th Korea- Japan foint Symposium on Cyclotrons and Nuclear Science


C(a,n)16O reaction studied by the

The 4th Korea- latxtn Joint Symposium on Cyclotrons and Nuclear Science
KOMAC H~ Beam Extractor for Cancer Therapy Hyo Eun Ahn
Korea Atomic Energy Research Institute, P.O. Box 105, Yusong, Taejon, Korea 305-600 email:
Abstract New scheme for a beam extraction is developed to extract a=20 negative hydrogen ion beam at 260 MeV from the KOMAC=20 (Korea Multi-purpose Accelerator Complex) linear accelerator, which produce both 18 mA protons (H + ) and 2 mA negative hydrogen ions (H~)=20 with energies up to 1 GeV. The negative hydrogen ions are extracted by a stripper magnet and the=20 un-extracted ions are returned to the linac. The main feature of this extractor is its ability to regulate the intensity of the extracted beam with the stripper magnet. The extracted 260 MeV beam will be used=20 for cancer therapy.
High Current Heavy Ion Cyclotron System Takeshi Katayama Center for Nuclear Study, School of Science, University of Tokyo Beam Physics and Engineering Laboratory, RIKEN
Abstract To develop a new phase of low energy heavy ion physics, it is intensively discussed at CNS to construct a high current heavy ion cyclotron accelerator system. The target specification of new accelerator system, is 6MeV/u for Xenon ion with average current 1 puA, and lOMeV/u for Oxygen ion with current of 100 puA. To accelerate such high current ion beam in the cyclotron system, it is found that the main accelerator should be separate sector cyclotron with K number 110, and the injector for that cyclotron should be a RF quadrupole linac. The main reasons of this selection are; to compensate the space charge problem in the injection energy at cyclotron, the injection energy should be high enough, and secondly to assure the high extraction efficiency from the cyclotron the turn separation should be large enough. The average magnetic field is set at relatively low and the RF acceleration voltage is high. To install the two RF cavities and extraction devices, the separate sector cyclotron is a most promosing candidate. In this report we will describe the details of design of cyclotron+RFQ injector system as well as the space charge problems in the beam transport line, cyclotron and RFQ linac.

[1] I. Blomqvist and J. M. Laget, Nucl. Phys. A280, 405(1977). [2] Kr. T. Kim et al., Phys. Rev. C38, 2366(1988). [3] R. H. Landau, Comput. Phys. 28, 109(1982).
Performing Org. Report No. KCCH/MR-021/99 Title/Subtitle Sponsoring Org Report No. Standard Report No. IMS Subject Code
MC-50 AVF cyclotron operation
Project Manager and Dept. Researcher and Dept
Kim Yu-Seok (Cyclotron Lab.)
Chai Jong-Seo(") Bak Seong-Ki(") Park Chan Won(") Jo Young Ho (") Hong Seong-Seok (") Lee Min-Yong (") Jang Ho Ha(")
Pub. Place Page Note Classified Sponsoring Org. Abstract (About 300 Words) Open(O), Outside( ), Class Report Type Contract No. Operating Report 66p Pub. Org. Fig. Table KCCH, KAERI Yes( O ), No( Pub. Date Size 2000.1
The first cyclotron in Korea, MC-50 cyclotron is used for neutron irradiation, radionuclide development,production and material and biomedical research. 50.5MeV and 35MeV proton beam have been extracted with 20-60M- A total of beam extraction time are 1095.7 hours. 206.5 hours are used for the developments and 663.8hours are for radionuclide production and development and 225.4 hours for application researches. The shutdown days are 23days.Fundamental data for failure decrement and efficient beam extraction were composed and maintenance technologies were developed.
Subject Keywords (About 10 Words)
cyclotron operation, maintenance,proton, accelerator, radioisotope

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Physica E 6 (2000) 636639
Two-component cyclotron resonance in bilayer quantum Hall systems
Kenichi Asano , Tsuneya Ando
Institute for Solid State Physics, University of Tokyo, 7-22-1 Roppongi, Minato-ku, Tokyo 106-8666, Japan
Abstract E ects of electronelectron interaction on two-component cyclotron resonance is studied in bilayer quantum Hall systems at absolute zero temperature. At high lling factors & 3=2, the low-frequency peak is pushed away to the low-frequency side with the increase of the interaction. This negative mode repulsion is opposite to a positive mode repulsion occurring at low lling factors. 1. ? 2000 Elsevier Science B.V. All rights reserved.
PACS: 78.66; 73.40.H Keywords: Quantum Hall e ect; Cyclotron resonance; Kohns theorem; Double quantum wells
1. Introduction Kohns theorem [1] is no longer applicable to multi-component systems, which consist of more than two kinds of electrons with di erent cyclotron frequencies. In such systems, cyclotron resonance (CR) is generally modied by electronelectron interaction in its positions and lineshapes. In this paper, interaction e ects on two-component CR are studied in asymmetric double quantum well (QW) systems in quantum Hall regime by means of a numerical diagonalization method. Interesting behaviors were observed in CR in Si (0) inversion layers, in which there are two kinds of
Correspondence address. Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan. Fax: +81-3-5841-7587. E-mail address: (K. Asano)
electrons with di erent masses because of multi-valley structure of conduction band [2]. A Fermi-liquid theory approach predicted that electronelectron interaction gives rise to a mode repulsion with intensity transfer [3]. A Boltzmann equation approach showed that electronelectron scattering which is important at high temperatures leads to merging of two peaks, i.e., a motional narrowing [4]. In GaAs=AlGaAs heterostructures, an up-spin electron has slightly larger cyclotron frequency than a down-spin electron. In the extreme quantum limit, an interesting mode repulsion behavior was observed experimentally [5] and analyzed theoretically [6]. In previous papers [7,8] interaction e ects on spin-split CR were studied in a quantum Hall regime. It was shown that spectra are categorized into three types of behaviors, a positive mode repulsion, a negative mode repulsion, and a motional narrowing, depending sensitively both on the lling factor of
1386-9477/00/$ - see front matter ? 2000 Elsevier Science B.V. All rights reserved. PII: S - ( ) 5 - 6
K. Asano, T. Ando / Physica E 6 (2000) 636639
Fig. 1. Schematic gure of bilayer system.
up- and down-spin electrons and on temperature. In this paper, we shall consider two-component CR in bilayer systems where the strength of intralayer and interlayer interactions can be controlled independently. Some experiments have been performed in such systems and have shown intriguing results (see for e.g. Ref. [9]). 2. Model and method An asymmetric bilayer system is illustrated in Fig. 1. The cyclotron frequency !n in the narrow QW is slightly smaller than frequency !w in the wide QW because of a nonparabolicity of the conduction band, i.e., = !w !n 0. We consider a rectangular system with a nite area ab = N under periodic boundary conditions, where the integer N denotes the number of ux quanta passing through the system and a and b are its linear dimensions. The lling factor of the layer i (=w; n) is dened by i = Ni =N , where Ni denotes the number of electrons in the corresponding layer. The total lling factor is dened by = w + n = Ne =N with the total electron number Ne = Nw + Nn. The spin of electrons is completely neglected. The potential energy between two electrons located in layers i and j is given as v(r) = 4 e2 r 2 + d2 (1

Fig. 2. Some examples of calculated CR spectra for d= = 0. (a) w = n = 1 and (b) ( w ; n ) = (1=2; 1). 8
where r is the distance between two electrons projected onto a two-dimensional plane, d is the distance between the layers, e is the electron charge, and is the background dielectric constant. Thus, intra- and inter-layer coupling of CR modes are characterized by intra = EC = and inter = intra = 2 + d2 with EC = e2 =4 , respectively. The case of vanishing d is exactly the same as that of the spin-split CR considered previously [7,8]. We shall consider the case that both and EC are much smaller than the averaged cyclotron energy (!w + !n )=2. All possible initial and nal states and their energies are obtained by numerical diagonalization and the dynamical conductivity is calculated by the use of the Kubo formula. Because of the moment sum rule, the rst moment of spectra is independent of interaction and given by !m = ( w !w + n !n )=. 3. Results The dynamical conductivity is calculated under the conditions 46Nand a=b = N0 =4, where N0 = Max(Ne ; 2N Ne ) and a=b is the aspect ratio.
Fig. 3. CR spectra calculated at
when d= = (a) 1, (b) 1:5, and (c) 2.
Fig. 4. CR spectra calculated at (
= (1=2; 1) for d= = (a) 1, (b) 1:5, and (c) 2.
The results are weakly dependent on N0 and a=b as long as N0 & 4 and a=b 1. The spectra are shown by histograms with width =100 (gray spikes) and a convolution with a Lorentzian with width =5 (solid lines). Fig. 2 shows some examples of spectra at ( w ; n ) = (1=8; 1=8) and (1=2; 1) for d= = 0. The results are the same as those of spin-split CR if w and n are replaced by and , respectively, and exhibit a posi-
tive mode repulsion. In fact, both peaks are shifted to the high-frequency side with the increase of the interaction, the frequency shift of the high-frequency peak is much larger than that of the low-frequency peak, and the intensity is transferred to the low-frequency peak. Resulting spectra at ( w ; n ) = (2=16; 2=16) for d= 0 are shown in Fig. 3. In this case, CR exhibits a positive mode repulsion similar to that for
d= = 0. The coupling strength between two CR modes is mainly determined by the inter-layer interaction decreasing slowly with the increase of inter-layer distance d. In this regime, electrons are separated from each other and CR transition can be approximated as excitations localized around a minimum point of an e ective potential formed by electrons in the other layer. As a result, the e ective cyclotron frequencies of both the CR modes are enhanced. Fig. 4 shows results at a high lling factor ( w ; n ) = (4=8; 8=8). CR spectra tend to show a negative mode repulsion behavior, i.e., both peaks are shifted to the low-frequency side and the low-frequency peak is pushed away to the low-frequency side with the increase of the interaction. This behavior is quite opposite to the positive mode repulsion exhibited by the corresponding spin-split CR spectra at ( ; ) = (4=8; 8=8) as shown in Fig. 2(b). The correlation between two CR modes rapidly decreases with the increase of inter-layer distance and the spectra at d= = 2 show only a slight e ect of interaction even when EC = 100. In the case of spin-split CR, there is a wide region in the lling-factor space where CR exhibits a motional narrowing behavior and such a negative mode repulsion appears only in special cases [8]. In the bilayer system with d= & 1, the intra-layer correlation of electrons is much larger than the inter-layer correlation and inter-layer overlapping has to be increased to reduce large overlapping of the cyclotron orbits in the same layer. As a result, CR transition is likely to occur at a maximum point of the e ective potential formed by electrons in the other layer. This presumably enhances the negative mode repulsion behavior.

4. Conclusion Two-component CR has been studied in bilayer quantum Hall systems at absolute zero temperature. At low lling factors.1, spectra show a positive mode repulsion, while they are inclined to show a negative mode repulsion at high lling factors & 3=2. More extensive calculations covering the whole lling-factor space and temperature are now underway and will be presented elsewhere. Acknowledgements This work is supported in part by the Japan Society for the Promotion of Science (Research for the Future Program JSPS-RFTF96P00103). One of the authors (KA) is supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists. Numerical calculations were performed in part on FACOM VPP500 in Supercomputer Center, Institute for Solid State Physics, University of Tokyo. References
[1] [2] [3] [4] [5] [6] [7] [8] [9] W. Kohn, Phys. Rev. 123 (1961) 1242. H. Kublbeck, J.P. Kotthaus, Phys. Rev. Lett. 35 (1975) 1019. Y. Takada, T. Ando, J. Phys. Soc. Japan 44 (1978) 905. J. Appel, A.W. Overhauser, Phys. Rev. B 18 (1978) 758. G.M. Summers, R.J. Warburton, J.G. Michels, R.J. Nicholas, J.J. Harris, C.T. Foxon, Phys. Rev. Lett. 70 (1993) 2150. N.R. Cooper, J.T. Chalker, Phys. Rev. Lett. 72 (1994) 2057. K. Asano, T. Ando, J. Phys. Soc. Japan 65 (1996) 1191. K. Asano, T. Ando, Phys. Rev. B 58 (1998) 1485. K. Ensslin, D. Heitmann, M. Dobers, K. von Klitzing, K. Ploog, Phys. Rev. B 39 (1989) 11179.



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