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ú{}CNOreBpwï Vol. 22 No. 1 2005 (3_11) ¬ÁWAFáC³údvY}ɨ¯é÷±q̮ƻ̧ä iðàj vY}Ì÷±q®ÌîbI_ δ C Dynamics of Fine Particles in a Complex Plasma Osamu ISHIHARA Abstract Dust particles in a plasma are charged either negatively or positively and are subject to various types of forces in a plas ma, including a drag force by plasma particles and a force due to collective nature of a plasma. Dust particles are found in layers in ground experiments balanced dominantly by the gravitational force and the electric force, while dust particles in the gravitationfree environment form three dimensional structures subject mainly to forces of ion/neutral drag and the electric eld. Dynamic motion of ne particles in a complex (dust) plasma is reviewed with the emphasis of collective nature of plasmas. A. V¤¯CC¤¯Éà©Â©ÁÄ¢éDܽFoª¯Ìa ͶßÉ ¶É[©©íÁÄ¢éÂ\«àwE³êÄ¢éD¯Í¯ FóÔɨ¯é 1 ~NöxÌ_Xg÷±qÌâè Ôªq_̧xªÅa¶·éª¯Ôªq_ÌüÓɶ Í X s b c A [ i Lyman Spitzer j Æ A F [ Ý·éFoªOüÉ ½èdq¹ÆÈèdqðúo iHannes Alf ávenjÉæÁÄ©çÚ³êÄ¢½D1940 µCÜíèÉ fÌd£Ìæð`¬µÄ¢éÆl¦çêÄ NãÉXsbc@[ͯԨ¿ÌÅ_Xg÷±qªÑd ¢éDFT¸@{CW[ 2 Íy¯Ì B ÂÉCS ·éßöÉ¢Ä_¶COüÆËÉæéõdøÊÉæé ©çúËóÉoÄ¢étiâjÌæ¤ÈX|[NÆÄÎê ³ÌÑdÌÙ©ÉCvY}±qÆÌÕËÉæè_Xg÷ éeªñ]µÄ¢é±Æð¦µÄ¢½D{CW[ªy¯ ±qÍÉÑd·é±ÆðwEµÄ¢é1)D¯ÔvY} ÉßÃÆX|[N;é¢wiÉeÌæ¤É©¦C{C ÍåÉ f©çÈèCd¢´qÍ_XgƵįÔóÔÉ W[ªy¯ðÊߵĵܤÆX|[NÍüÓæèྠ¶ÝµCd³fðärI½Üñ¾¯Ô¨¿ÌåÈ f éP¢Ä©¦½ÌÅ é3)DX|[NªÅ«éÌÍy¯ ªq_©çVµ¢¯ª¶ÜêéÆl¦½ÌÅ éDܽ ÌÂæèñ80 km ãÌƱëÅÃdIɢĢéÑdµ 1954NÉAG[;znÌN¹É¢ÄÌÌ ½÷±qª´öÅ éÆl¦çêC_Xg÷±qÉ墀 ÅCd£KXªÃkµC_Xgi÷±qjÆÈèC»êª Ì»¡ª©«½Äçêé±ÆÉÈÁ½ÌÅ éD±Ìsv WÜÁÄ_XgvY}¯_idusty plasma cloudsjÆÈ cÈ»ÛÉεÄC2004N 7 Éy¯É µ½y¯T¸ èC´n¾zn`¬Éʽ·ðð_¶Ä¢é2)D»Ìã @JbV[j_zCwXÉÍ÷±qϪ̽ßÌv[ ·¢ÔðoÄC_Xg÷±qªÚðÑéæ¤ÉÈÁ uàÚ³êĨè»Ìà½ç·ÊªúÒ³êÄ¢½ ½ÌÍ1980NãÉÈÁÄÄÌ NASA [FT¸@{C ªC¡ñÍX|[Nͩ©ÁĨ縳çÉ»Ìäª[ W[ª¾znf¯ÌÚ×Èf[^ðà½ç·æ¤ÉÈ ÜéÊÆÈÁÄ¢éD èCnbuF]¾ª³Ü´ÜÈVÌÌfðÁÄ êûCnãɨ¢ÄÍ1980Nã㼩缱̻¢ÉÖ éæ¤ÉÈÁÄ©çÅ éDf¯ÌÂÌÚ×ÈϪÉæ AµÄ¢»w½«ðàÂvZXvY}Ŷ· è÷±qªFóÔɨ¢ÄdvÈ«ðµÄ¢é±Æª é~NTCYȺÌ÷±qÌðß®ÁĤªi ¾ç©ÉÈÁÄ«½ÌÅ éDÑdµ½f¯Ô÷±qÍf ßçêÄ¢½4)D»¤µ½÷±qÍâGNgjN ¯ÌÂÆÝìpµCܽ©gð`¬·éÂ\«ªwE XfoCX»¢ÌåGÅ Á½D»ñÈÅ1986NÉv ³êÄ¢éD¢ÜÅÍf¯ÌÂÍy¯ÌÝÈç¸CدC Y}Ì÷±qÍN[iqiCoulomb latticejðìé ¡l§åwåw@Hw¤@ §240_8501 ¡lsÛyJæíÕä79_5 Faculty of Engineering, Yokohama National University 79_ 5 Tokiwadai, Hodogayaku, Yokohama 240_8501, Japan (Email: oishiharynu.ac.jpj \ 3 \ 3 δ ±Æª\ª³ê5)C1994NÉÈÁÄCðª»ë¦Îv C ð^¦éD±±Åè b0 Í Y}Å÷±qªK¥IÈ\¢ðÆéÆ¢¤N[» b0 iCoulomb Crystaljª©³ê½ÌÅ é6_8) D±±É« ÄÑd÷±qªvY}ÆÝìp·é±ÆÉæÁÄÅ« é¡nƵÄÌVµ¢¤Êª¾ç©É³ê¾µ½ÌÅ é 9_ 13) D{eÅÍvY}Ì÷±qÌ®ÉÅ_ð Ä é½ßCæ 2 ßÅܸ÷±qüÓÌvY}±qÌ^®ð Zd Zs e2 4pe0msn2 (6) Å^¦çêéDi3)®ÉîÃCIO¹ÌlvZ©ç ÷±qßTÅÍCIÌUpÍñíÉå«Èé±Æª ¦³êÄ¢é14)D l¦éƱë©çͶßéDæ 3 ßÅvY}±qÌ^® C. ÷±qÌÑd ÌÊƵĨ±é÷±qÌÑdCæ 4 ßÅ÷±qÉyÚ ·CIïR©çà½ç³êéÍð_¶éDæ 5 ßÅ÷± ÷±qªvY}Éu©ê½Æ«ÌÑdÊÍdqÆC qÔÉøÍCæ 6 ßÅ¥êÌ÷±qÌ^®C»µÄ IÌd¬ªÅ¿Áµ ÁÄCvY}©çø«Þd¬ ÅãÉN[NX^[Ì\¢`¬É¢ÄÐî·éD ª 0 ÉÈéÆ¢¤ð©çßé±ÆªÅ«éD÷±qð B. ¼a a Ì ÆµÄCCIªp^®Ê mi bcn ðÁijÀ ÷±qüÓÌvY}±qÌ^® ©çßÃÆ«É÷±qßTÅO¹ªÈ°çêÄ÷±q 1 ~NöxÌ嫳Ì÷±qªvY}ɶݷ \ÊÅÚ·éæ¤ÉiÞàÌÆ·éD»ÌÆ«ÚüûüÌ éÆC³Ìd×ðÂd¢CIæèÍé©É®d ¬xð nt Æ·éÆGlM[Æp^®ÊÌÛ¶imi bcn q̽ßÉ÷±qÍÌdÊð¾ÄCCIðЫ¯C mi antj©çÕËp[^ dqð´¯éæ¤ÉÈéD»±ÅܸÉÑdµ½÷± ( 2b0 a bca 1{ qÆvY}×d±qidqCCIjÌÕËfÊÏð ßĨ±¤DvY}Åd× Zd e ðÂ÷±qªìé| ) 1/2 (7) eVÌÅÌ¿Ê msCd× Zs eiCIÉεÄÍ ð¾éDIa ð³Ü´ÜÈ`Å÷±qɬêÞd¬Æ·é siCdqÉεÄÍ se Å Ze|1jðÂvY}± Æ qÍ^®GlM[ dr 2 1 1 ms ms dt 2 2 || [r· {(r _u) ] 2 2 a (1) (8) a ª¬è§ÂDd¬ÉÍdq¨æÑCId¬Cñdqú oCMdqúoCõdqúoÆ¢Á½à̪ñ^·é±Æ Æ|eVGlM[ U(r) I 0, ÉÈéªC±±ÅÍdqd¬ÆCId¬ÌÝðl¦éD Zd Zs e2 |r/l e 4pe0r (2) D ¬x n ðÂCIª\Ê|eV q(Zd e/4pe0a) ð¼a a Ì÷±qÉßÃÌLøÕËfÊÏÍ si ðÁÄ¢éD±±Å lD ÍfoCÕÁ·Ce0 Í^óÌU pa2 (1|2Zi eq/mi n2 ) ÆÈéD¯lÉ¿Ê me ÌdqÉε d¦Å èCÊuxNg r(r, u) Í÷±qð´_ÉÆ ÄÍ sepa2(1{2eq/men2) ÆÈéD÷±q\ÊɬêÞ Á½ÉÀWÅ\³êÄ¢éDGlM[Æp^®ÊÛ¶Ì dq̽Ïd¬Í¬xÌϪæÔði|2eq/me )1/2`Æ ÖW©çvY}±qÌO¹Í µÄCIe|çseenfe(v)4pn2dn Å^¦çêéDܽCIÌ r 2 ( ) ( ) 2 du dr b r 2 1 1|Ueff(r) ½Ïd¬ÍϪæÔð 0`ƵÄCIi çsi Zi enfi (v)4pn2 (3) dn Å^¦çêéDdq̬xªz fe (v) ð·x Te ðà ûIÈ}NXEFªzCCI̬xªz fi(v) Í· Å çí³êéD±±ÅÛ¶ÊÍ n ð³ÀÅÌvY} x Ti ðà¿Cêûüɬê̬x vf (nf |vf |) ðÂ} ±q̬xƵÄCEmsn /2, pums bn ƨ¢½Db ÍÕ NXEFªzÆ·éÆC÷±q\ÊɬêÞd¬Í 2 Ëp[^ÅCKi»³ê½Àø|eVÍ Ueff(r) ( r ){ m n b 2 2U(r) s 2 I|2 p a2enenTe e eq/kT { p a2Zi eninTi e { 2 f ~ e |n /n { p (4) Ti [n {2n (1| kT )]erf(n )} nf Ti nTi f 2Zi eq i nf Ti (9) Å éDi3)®©ç¾ç©Èæ¤É Ueff (r) ª 1 ÉÈéÆ «Cdu/dr ÍUµCvY}±qª÷±qÉÅÚß·é Æ Èé D± ±Å ne Íd q§ xCni Í CI §x CnTi ð (2kTi /mi )1/2 , nTe (2kTe /me)1/2 , erf(nf /nTi ) Íë·ÖCk 2b0 | r e l r D 4 ( )|1 b r 2 J. Jpn. Soc. Microgravity Appl. 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Vk ve0e(k, v) j1 2 Æ çí³êé20)D¢ÜCI̬ꪶݵCCI¹ (21) ÖÍ k 2De v2pi , 2| k (v|k¥vf)2 ÆÈéDq1 V, r3~103 kg/m3 ÌÆ«C r1r21~10|4 m2 (25) Xg÷±qÉæÁÄ`¬³êé|eVÍu\tE qÔ£ªfoC·Éä×Ä\ª¬³¢Æ«idálDjCr1 1/2 d 3xne(x) |A\ûö®Ìt[G_vXÏ·Éæè ÌÜíèÉ éCI̶ÝÉæèN[½ÍÍ®S r2r Å q1q2q ÌêÉÍ f 1 V Í»ê¼ê½ÏÌCI§xCdq§xð\µÄ¢éD_ ÉÕÁ³êdÍÉæéø;¯ª«¢ÄéDêûC÷± 9e0 4pG (24) ÆÈéD±±Å N/Vnd Í_Xg̱q§xÅC ÈéÖWª éÆ«ñÂÌ÷±qÍÝ¢Éø«¤±ÆÉ r1r2 (23) r1r21 cm e(k, v)1{ i22) (27) Æ çí³êéD±±Å vf ÍCI̬ê̬xCkDe Í ÌÆ«÷±qÔÉøͪ«C r1r2 1 cm ÅËͪ dqfoCg·Ìt kDe( ne e2/e0kTe)1/2, vpi ÍCIv ±ÆÉÈéDFóÔÅÍd£KXª÷±qÌíÆÈéj Y}üg vpi ( ni e2 /e0mi )1/2 Å éDi26)®Í v0 ðSƵÄÃkicondensationjµÄ\ªÉå«Èé Æ e(k, vl(k))0 ð½·æ¤È vvl(k)(kEvf}vk) ƨݢÉø«¤æ¤ÉÈèCÃWiagglomerationj ɨ¢ÄÉðÂD±±Å vk vpik/ k2{k2DeDv0 ÌÉ µÄ÷±qͳçÉå«ÈÁÄ¢DêÊIÉÍñÂÌ ªñ^·é|eVÌóÔÏ»Í q(x)q0 (x){qw ÷±qÍÝ¢ÌüèðñèȪçæÉp^®Êð¸¢C (x) ÆÈéD±±Å ÅãÉÐÆÂÉ̵Ģ±Æª\z³êéDÐÆÂÌ q0(x) ÷±qªXÉå«ÈÁÄ¢Æ(22)®©çCæ謳 ¢÷±qðЫ¯é±ÆªÅ«éæ¤ÉÈèC±¤µÄ e ik¥(x|x ) Zd e N , e0V j1 k k 2{k 2De qw(x) ½Ì¬³È÷±qªå«ÈòÌüèðÜíèC_Xg_ ªÅ«é±Æªl¦çêé2)D j e ik¥(x|x ) Zd e N v2k . e0V j1 k k 2{k 2De (k¥vf)2|v2k j (28) ¼±Ì»¢ßöâÀ±ºÅµ¤÷±qÍ 1 ~Nöx ¢ÜCI̬êð|z ÌûüÉÆèCnÌÌÏð³Àå Ì嫳ŠéDµ½ªÁÄ(22)®©çdÍÉæéøÍÌ Vçd 3k/(2p)3 ÆµÄ k_óÔÌûÊpûü Æl¦k ¨ V¨ 6 J. Jpn. Soc. Microgravity Appl. Vol. 22 No. 1 2005 \ 6 \ vY}Ì÷±q®ÌîbI_ ÉÎÌÈ~ÀWnir, zjÅCvY}ÌÕÁðl¶µ ÌóÔÏ»ðã©çݽàÌÆ 2 ³óÔÉüÉæè ÄϪæÔðÀèµÄ]¿·éÆóÔIÉU®·é|e \µ½àÌÅCFig. 1b ÍÌ|eVª©¦éæ¤ Vð¾é Épxð©¦Ä\µ½àÌÅ éD±±ÅÍ÷±qð_d 20) f M2 Zd e qw( r, z) 2 2pe0 ( M |1)3/2 2 1/lD 0 ×Æl¦½ªC嫳ð³Å«È¢æ¤È÷±qªV[ dkÛ(kÛ/kDe)2J0(kÛr) ~sin [kÛz/ M |1]. XÌæ¤ÈdêÌÈ©É éÆ÷±qͪÉ𨱵oÉ (29) q[g p ðàÂÉÈéDdêÌ嫳ð E Æ· éÆ÷±qª¼a a Ì ó±ÌÈçoÉq[gÌå ±±Å}bn M|vf |/Cs iCs ÍCI¹¬jCJ0 (kÛr) «³Í 4pe0a3E Å^¦çêCUd¦ e ðàÂUdÌÈç Í 0 ÌxbZÖÅ éD±ÌÕgÌæ¤Èæ[ª 4pe0mi|1{e/e0)/(2{e/e0jna3E Å^¦çêéD±Ìo ƪÁ½`ðµ½óÔU®|eVÍCÃTIÉÍq Éq[gªìé|eVÍ£ r £ê½Æ±ë Õêiwake potentialjƵÄ÷±qªCI¬Ì év ÅC÷±q©çϪ_Éü¯½xNgð r Æ·éÆ Y}Å`¬·é|eV\¢ÆµÄmçê20_22)C ÊqÍwIÉÍñÂÌ_Xg÷±qªtHmiCI¹ q gÆ¢¤vY}ÌWc^®ðÊq»µ½àÌjðâèæ p¥r 4pe0r3 (1{l ) exp (|r/l ) r D D (30) èµÄÑ¢ĢéàÌÆðÅ«é23,24)D÷±qª} Å èC±ÌoÉq[gªqÕêÉyÚ·øÊà_ bn1.5ÌCI¬Éu©ê½Æ«Ì|eVÌl ¶çêÄ¢é25)D qðir, zj½ÊÅ Fig. 1 ɦ·DFig. 1a Í|eV ±¤µ½qÕêÌo»Í±qV~ [VÅàmF ³ê26,27)CÀ±IÉàmF³êÄ¢é28)Dܽ¿Ê³Àå ÌñÂÌ÷±qªCI¬É¼Éu©ê½Æ«Ì±q V~ [VÅÍC÷±qÔ£ªdqfoC·öx ©»êÈãÉÈêÎwãɱ|eV\¢Íª£µ ½àÌÆÈè£UIÈ÷±qñªCI̬êÉÁÄ` ¬³êé±ÆªúÒ³êéªC÷±qÔ£ªdqfoC g·æèZÈêÎwãÌ|eVÍݢɱµ ¤±Æª¾ç©ÉÈÁ½29)D}bn M 2 ÌêÌV~ [VÌÊð Fig. 2 Æ Fig. 3 Ŧ·DFig. 2 Í ÷±qßTÌCI§xÌ\ÊvbgÅCFig. 3 Í|e V\¢ðg|OtB[\»Å\µ½àÌÅ éD A ÆLµ½Æ±ëͳÌ|eVÅCB ÍÌ|e VÌæð\·D÷±qÌwãÉÇIÈCI̧W ªªÅ«³Ì|eVð¶µÄ¢é±Æªí© éD vY}Ì«EÌæV[X̪Åͧxùzɺ¢C CI̬ꪶµCÉÑdµ½÷±qª»±É ê Î÷±qÌwãɳÌ|eVªÅ«C»±ÉÊÌ÷ ±qªÍ¢èÌ÷±q¯mÅø«¤±ÆÉÈéDÂÜ èqÕê̶Ýä¦É¬êÉÁ½÷±qÔÉøͪ ±ÆÉÈéDå«Èd×ðÑѽ÷±qÔÉøͪ ±ÆÍ_IÈ»¡ðø«N±µC¼ÌJjYÉæé øÍC½Æ¦Î¨IÉå«È÷±qªÇÆÈÁÄCI ̬xªzðÏ»³¹ÄÅ«éVh[øÊ30)CvY} ÌWc^®ðîƵĶ·éøÍ31,32)ÈǪ_¶çê Fig. 1 Wake potential behind a dust particle in the ion ow. Mach number M1.5. Threedimensional view of the potential structure and its projection on rz plane. (a) View from the positive potential. (b) Side view to show the oscillating potential. A large negative potential at the front, indicating the presence of a dust particle, is followed by a large positive potential and then an oscil latory nature in space. J. Jpn. Soc. Microgravity Appl. Vol. 22 No. 1 2005 Ä¢éD À±ºÅN[NX^[ª©Â©èC÷±qªdÍ ÆV[Xdê©çó¯éÍÌÂè ¢ÉæÁÄV[XÌÀ çê½Ì枯ãµÄ¢é±Æª¾ç©ÉÈèC ó ÌN[NX^[ðìé½ßÉ÷¬dÍÅÌÀ±ªs íêÄ¢éD»ÌÊ óÌNX^[ÍÅ«ÄàC^ñ ªóÉÈé{Ch̶ݪ¾ç©ÉÈÁ½33)D{Ch \ 7 \ 7 δ C ÍS©çO¤Éü©¤CI̬êÉæéCIÌïR Íiion drag forcejª÷±qðO¤É¨µâèCV[Xd êÉæédCÍÆÞèÁ½Æ±ëÅ ÌO¤ßTÉ÷± qªWÜé½ßÆl¦çêÄ¢éDvY}S©çOÉ ü©¤CI̬êªìéqÕêÉæÁÄ÷±qͬêÉ ÁÄêñÉÀñÅ¢ªC¬êÉε¼ÈûüÉ÷± qªÀÔ±ÆÉεÄÍ(28)®Ì|eV q0(x) ªñ ^·éMÍwIÈl@ÉæéøÍÌøʪñijêÄ¢ é34)D F. ¥êÌ_XgÌ^® ±êÜÅÍvY}ª÷±qÉyÚ·e¿ðSÉl¦ Ä«½D±±ÅÍ÷±q©gªd¥êÌÅ®lqðl ¦ÄÝéDvY}±qÍdqi¿Ê meCd×|eC§ x neC·x TejÆCIi¿Ê mi Cd× Zi eC§x ni C ·x Ti j»µÄ«±q©çÈèCRvbNXv Y}ÅÍ»ÌÉ_Xg÷±qi¼a a Ì C¿Ê§x rd C§x ndC¿Ê md Cd× QZd eC·x TdjªÍ¢Á Ä¢éD½Ìê Te Ti Td ª½³êÄ¢éD½Æ Fig. 2 Surface plot of the ion density, showing ion focusing be hind the dust particles, for three dierent separations D between two dust grains. D(a) 0.8 lDe (b) 0.4 lDe (c) 0.2 lDe. M 2 . Dust particles are placed perpendicu lar to the ion ow. (From Ref. 29) ¦ÎÀ±ºá·vY}â¯ÔóÔÅÍdq·xª eV ÉεÄCÀ±ºá·vY}Å Tdk0.03 eVC¯ÔóÔ ÅÍ Tdk0.003 eV Æl¦çêéD÷±qÌäd×Í ( )( |Q| |Zd| 3.1~10|3~ md 104 ) C/kg 5.2~10|13 kg md (31) ÆÈèdqÌäd× e/me1.8~1011 C/kgCzqÌäd× e /mp9.6~107 C/kgimp ÍzqÌ¿ÊjÆÍ á¢ÌàÌ Å éDa5 mm, rd1 g/cm3 Ì÷±qª|104 e ÉÑd· éÆ«»Ìäd×Í0.003 C/kg ÆÈéDRvbNX vY}ÅͽÏ÷±qÔ£ d(âak0.1 mm_10 mm) Æ vY}ÌÕÁ£ªóÔXP[ÆµÄ çíêÄ éDÕÁ£ÍCIªwi̳Ìd×ð^¦éÆ«Cd qfoC· lDe74.3~(1016 m|3/ne)1/2(kTe/1 eV)1/2 mm É æÁÄÁ¥t¯çêéDvY}ªdq·x Te CCI ·x Ti ÌM½tÉ éÆ«ÉÍ lDi ðCIfoC·Æ |2 |1/2 Å^¦çêéDvY}ÌWc µÄ lD (l|2 De {lDi ) ^®ð\·ÔXP[ÍvY}üú 2p/vpe k1.1~ (1016 m|3/ne)1/2 nsecCdqÆCIÌTCNgüú 2p/|vce |k0.36~(1 kG/B) nsec, 2p/vci k0.66~(mi /Zimp ) (1 kG/B) msec ðgÁÄ\³êéD_Xg÷±qnÌÔ Fig. 3 Contour plots of the plasma potential for two dust grains separated by four dierent distances. The plot is presented in the gray scale topographic style. Note that the potential wells (region B) are formed behind the dust grains. The potential wells merge together when the separation distance is less than the electron Debye length. (From Ref. 29) XP[Í_XgvY}üg vpd(nd Z 2d e2/md e0)1/2 Æ _XgTCNgüg vcd Zd eB/md ðgÁÄ« \³êéDlðüêÄ«\·ÆC ( )( ) ( 10 m ~ ( n ) msec 104 2p k2.38~ vpd |Zd| |3 1/2 11 d 8 J. Jpn. Soc. Microgravity Appl. Vol. 22 No. 1 2005 \ 8 \ a 1 mm 3/2 ) rd 1 g¥cm|3 1/2 (32) vY}Ì÷±q®ÌîbI_ ( )( ) ( 2p 104 k165~ |vcd| |Zd| a 1 mm 3 rd 1 g¥cm|3 )( ) 1 kG B vûüÉñ]·é³Üð\µÄ¢éD±ÌÆ« r0 Í lD sec (33) Éä×Ä\ªÉ¬³C¥ê̳ð^¦ép[^Í |Zd|eB/md0.17(k1/md )1/2C÷±q̬xÍvûüÉ 0.05 r0(k1/md)1/2 ÆÆÁÄ¢éD À±ºÉ¨¯é¥êÌ÷±qÌ^®ð¤·é±ÆÍ ÆÈèCÊíÌÀ±ºÅÌðÅÍvY}nÉä×Íé ©ÉäÁèµ½ÔXP[Å é±Æªí©éD±ê f¯óÔɨ¯é÷±qÌ^®ð\ª³¹éàÌÅ éD ÉεÄ÷±qnÌWc^®ÌóÔXP[ÍvY}n À±ºÉ¨¢ÄÍÃd|eVÉæÁÄSÉø«ñ ÉärµÄñíÉå«ÈàÌÆÈéD ¹éÍðìè÷±qð¶ßéªCf¯ßTÅÍåÈ À±ºÅÃd|eVÌɶßçê½¥ê f¯Ìdͪ÷±qðø«ñ¹Ä¢éDدÌüèÅV Ì÷±qÌ®ªÏª³êÄ¢éDÐÆÂÌ÷±qð©ê [[J[Eræ 9 a¯ªª¬ÍÉæèªôµC÷± ÎXsðµÄ¨èC»Ì´öƵÄÍCI¬Ì¬xV qªØ¯Ì¥êÌe¿ðó¯ÄüèðñÁÄ¢éÂ\«ª A35)â÷±q\ÊÌñÎÌÈÑd36)ª_¶çêÄ¢éDÜ ñ³êÄ¢é39)D ½XsðµÈªç ½©à¾znÌf¯Ìö]^®Ìæ G. N[NX^[Ì\¢`¬ ¤Éå«È~ð`±ÆàϪ³êÄ¢éD»ÌnÌn~ 1994NÉ©³êÄÈC¤ªÉsíêÄ¢é gjAÍ H 1 |p|Zd eA|2{V(x) 2md N[»ÅÍÉÑdµ½÷±qª\¢ðìÁÄ¢é (34) í¯Å éªC¯íÌd×ðÑѽ±qªÇÌæ¤È\¢ ðìé©Æ¢¤±ÆÍ20¢I̪©ç¤ÌÎÛÉÈÁ ±±ÅxNg|eV A(0, rB/2, 0) Í z ûüÉ Ä¢½DJ. J. Thomson ªÂóÉÀñ¾±qÌÀè«Éæ ¥êð^¦éàÌÅC è´q\¢ðྵæ¤Æµ½Ìª1904ṈÆÅ è40)C V(x) 1918NÉÍ E. Madelung ªÃdGlM[ÌvZ©çC 1 (Zd e)2 (k1r2{k2z2){ 2 j 4pe0|x|xj| ~exp ( | ) |x|xj| {md z lD I¨¿Ì\¢ð_¶Ä¢é41)Dµ©µLÀÌÌ Ýìp·é×d±qÌ\¢`¬É{iIÈ»¡ªªê¾ (35) µ½ÌÍܾÅß̱ÆÆ¢¦é¾ë¤DtÌwE\ ÍSÍð^¦é|eVi±±ÅCk1, k2 ÍèC 1979ÉÈÁÄ©çÅ é42)D1980Nãã¼C¼±ÌÌ÷× ÊÅdqª Wigner »ð`¬·é±ÆªÏª³ê½ÌÍ r 2x 2{y 2jCÕÁðl¶µ½N[|eVC»µ \¢ÁHZpÌWÉæèÊqhbg̤ªiÞÆC| ÄdÍ|eVðÜñÅ¢éDdÍÍ z ûüƵ½D eVɶßçê½dqÌæêéGlM[ªò ±Ì|eVÌÅÌ÷±qÍdÍÆ z_ûüÌÃd ÑòÑÉÈé±Æªí©èC´qjÌüèÌdqÌlqÆ ÍªÂè ¤ x_y ½ÊãÅCO¹ÉÁÄU®µÈªç~ Ä¢é½ßÌdqµ©¶ÝµÈ¢ÊqhbgÍlH ^®·é±Æªm©ßçêÄ¢é37,38)DFig. 4 ÍÐÆÂÌ ´qÆÄÎêéæ¤ÉÈÁ½DlH´q̤Í妧 ÷±qª¥êɼÈÊÅU®µÈªç¼a r0 Ì~üð |eVÌɶݷéLÀÂÌ×d±qÌìéÃT IÈnÌUé¢ð²×é±ÆÉηéDÅßC2 ³ Êqhbgɨ¯édqÌ Wigner »»ÆnðÌlqª V~ [VÉæÁĦ³êÄ¢é43) DêûC[ U[âpÌZpÌiàÉæèCIðgbvÆÄÎêé ¬³ÈÌæÉd¥êÉæÁĶßC»ÌÅCIª \¢ð`¬·é±ÆªÏª³êÄ¢é44)Dܽdê̶ ßðgÁ½ Paul gbvC¥ê̶ßðgÁ½ Penning gbvɶßçê½CIª³Ü´ÜÈ\ ¢ð`¬·é±ÆàmçêĨè45)CPenning gbvÉ æÁĶßçê½ñ«vY}ÌìéN[N X^[Ìk\¢É¢Äàc_ªsíêÄ¢é46)DvZ@ ðgÁIJaU®|eVɶßçê½âp³ê ½CIÌ\¢ªÚµ²×çêCŬGlM[ðÆé Fig. 4 Trajectory of a dust particle in a plane perpendicular to the magnetic eld, which is in parallel with the gravity. |Zd|eB/md0.17(k1/md)1/2. Initially a dust particle is injected in a clockwise direction with velocity 0.05 r0(k1/ md)1/2. (From Ref. 38) J. Jpn. Soc. Microgravity Appl. Vol. 22 No. 1 2005 zuƵÄÀèÈ\¢ª¾ç©É³ê46)C¯SóÌ k\ ¢ªÅ«é±Æà©o³ê½47)D vY}÷±qªÂéN[NX^[Ì\¢Í CCD JðʵÄ÷áÅϪÂ\Æ¢¤IÈX \ 9 \ 9 δ C êÎ70ÂÌÉͳ 6 p`ðµÄ¨èC134ÂÌÉͳ 8 p`ÌSÉÐÆÂCÂÜè 3 ³IÉÍSÉê{Ì ½ª¶Ý·é±Æð¦µÄ¢éD H. ¨ í è É vY}ɶݷé÷±qÌâèÍFɨ¯é¯Ì `¬ÌâèÅéçc_ÌÎÛÉÈÁÄ¢½ªC1990N ã¼Î©çvY}vZXâÀ±ºÅ÷±qð§äµÄ ¶¬C¬·³¹C»Ì®ð²×é±ÆªÅ«éæ¤ÉÈ ÁÄ«½DHwIpÌÊÆîb¨ÌÊ©çC÷±qv Y}̤ÍÓ~IÉißçêÄ¢éD÷±qª½¶ Ý·évY}ðCvY}Æ_XgWcÌ¡nÆµÄ ¨¦CRvbNXvY}Æ¢¤¾tàægíêé æ¤ÉÈÁÄ¢éD{eÅÍ÷±q®ÌîbI_É ¢ÄC÷±qüÓÌvY}±qÌe¿CvY}Wc» ÛÌe¿C|eVÌe¿C¥êÌe¿C»µÄ÷± qÌ\¢`¬Æ¢Á½âèÉ¢Ä_¶½D {¤Íú{wpU»ïÌÈw¤ïîÕ¤ B(2) Fig. 5 16340179̬ð¾Äißçê½D Spindleshaped Coulomb cluster formed in the molecu lar dynamics simulation. The left column contains 70 dust particles, while the right column contains 134 dust particles. (a) Side view. (b) Projected view. (From Ref. 52) Ql¶£ 1) 2) P[ð±ƩçV½È¤Þ¿ÆµÄ}¬É Ú³ êéæ¤ÉÈèCFvY}̤ÆÀ±ºvY}¤ ÌÚ_ª©o³êéæ¤ÉÈÁ½DÀ±ºvY}Å N[»ª`¬³êélqâC¢Á½ñ`¬³ê½ N[»ªnð·éßöª±êÜÅÉϪ³êÄ¢ éD±Ì]Ú»ÛÌϪÍÂXÌ÷±qÌ^®»ÌàÌ ðÇÁ©¯ÈªçϪūéÆ¢¤±êÜÅÉÍȢϪ ððìèoµÄ¢éDN[NX^[̤ÉÍÀ ±ºÉ¨¯éÀ±ÌÝÈç¸Cªq^®_âeJ Æ¢Á½è@ÉæéRs [^V~ [Vàsí êÄ¢éD»êÉæè|eVÌɶßçêÝ 3) 4) 5) 6) 7) 8) 9) 10) 11) ¢ÉN[½·é×d±qÌ 2 ³C3 ³\¢ª¾ ç©É³êÄ¢éDSÉü©¤ÎÌIÈ|eVÉ Â¶ßçê½ 2 ³\¢ÅÍÂó\¢48)C3 ³Åͱ 12) 13) qɶÄk\¢CÌS§û\¢ªñ³êÄ¢é49)D ܽcûüÆ¡ûü̶ß̳ðϦé±ÆÉæÁ Ä 2 ³Âó\¢ªwó\¢ÉÚsµCO³IÈk\¢ ÉÈé±ÆªeJV~ [VÉæÁĦ³ êÄ¢é50)D½p`\¢C½ó\¢É¢ÄÌV~ [ Vàñ³êÄ¢é51)D±±Åͪq®Íw@Éæé V~ [Vũ©Á½aóÌN[»Ìá ð°é52)DFig. 5 Í70ÂÆ134ÂÌ÷±qªdÍøÊð ³µ½(35)®ik1/k25jÅ^¦çêé|eVÌ 14) 15) 16) 17) 18) 19) Éü³ê½Æ«É`¬³ê½àÌÅ éDe}ð© 10 J. Jpn. Soc. Microgravity Appl. Vol. 22 No. 1 2005 \ 10 \ L. Spitzer Jr.: Physical Processes in the Interstellar Medium, Wiley, New York, 1978. H. Alfv áen: On the Origin of the Solar System, Oxford University Press, 1954. B. A. Smith et al.: Science, 215 (1982) 504. A. 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