O ZBEKISTON RESPUBLIKASI OLIY VA O RTA AXSUS TA LI VAZIRLIGI SAARQAND DAVLAT UNIVERSITETI Qo l yozma huquqa UDK 537.3.33.534.8 URINOV JASHID ORTIQOVICH YARIO TKAZGICHLARDA ULTRATOVUSHNING YUTILISHI VA KUCHAYISHI HAQIDA 5A4-Nazary za agstr aam arajasn olsh uchun yozlgan ssrtatsya Ilmy rahbar: otsnt Parayv O.P. Samarqan-6
agstrl ssrtatsyanng ANNOTATSIYASI Dssrtatsyaa ssq ltronl yarmo tazgchlara gronam yaqnlashuva tovush to lqnnng uchaysh taqq qlngan.bunay yarmo tazgchlara tarqalayotgan tovush to lqn yzoltr mayon hosl qlb,bu mayon tovushnng ast ntnsvllara ham o tazuvchan ltronlarn qztb yuborar an va natjaa taqsmot unsyas szlarl arajaa nomuvozanat holga lar an.bunay taqsmot unsyas yzoltr yarmo tazgchlarnng asosy nt aramtrlarn muhm o zgarshga olb la.oata bunay nt aramtrlaran ltronlarnng lamlg,otazuvchanlg,ltronlarnng ry tzlg va boshqalar bunay moalara tovush to lqnnng yutlsh va uchayshn oalovch Uaytnng yutlsh otsyntga ra va natjaa ltronlarnng qzsh bu ormulan tamoman o zgartrb yubora. Dssrtatsyaa yuqor lamla ga bo lgan va ch tv massal n InSb turag yarmo tazgchlara tovush to lqnnng tarqalsh o rganlgan.bunay yarmo tazgchlarnng tanlab olnshga sabab shu,ulara jua ast tmraturalara nrgyanng rlasatsya vaqt ancha an,ya n atta bo lar >> tngszlg o rnl bo la.dma,yarmo tazgch ltronlarnng o zaro to qnashuv shunchal tz, natjaa ltronlar mulslarnng o zaro to qnashuv orasag vaqt yo mulsnng rlasatsya vaqt з jua ch bo la.yuqorag tngszl moa ltron sstmasa nrgyanng to lansh,oqbat natjaa ltronlar qzvunng yuzaga lshga olb la.
Annotaton o ssrtatson A nonlnar thory o acoustc - lctrc cts or th soun wavs o larg amltu s vlo or smconuctors wth small ctv masss an larg nrgy rlaaton tms o lctrons whr th omnant ty o acoustc-lctrc nonlnarty s u to th statonary hatng o th lctron gas by soun wavs an to th nnc o th ntc cocnts on th lctron tmratur. It s shown that nnc o th lctron absorton cocnt, acoustc-lctrc currnt, acoustc-lctrc l tc. on th soun ntnsty s qut rnt or varous lctron momntum an nrgy scattrng mchansms an s also rnt rom corrsonng nncs or th cas o th usual consnt ratonal acoustc-lctrc nonlnarty. In artcular, th nnc o th acoustc-lctrc currnt on th acoustc-lctrc l may b surlnr-contrary to th cas o th connsatonal nonlnarty. It s also shown that th aaranc o ths «hatng» nonlnarty movs o th onst o consnt ratonal nonlnarty. Th nlunc o a strong lctrc l on th nonlnar acoustc-lctrc hnomna s stu. It s shown that by hatng th lctron gas th lctrc l rucs both th consnt ratonal an th «hatng» nonlnar acoustc-lctrc ct an thus wns th ynamc rang o th ultrasonc amlr.
UNDARIJA Krsh 4 I-BOB. PYEZOELEKTRIK YARIO TKAZGICHLARDA ULTRATOVUSHNING TARQALISHI.. Pyzoltr rstallara ultratovushnng ltronlar blan o zaro ta sr. Eltronlar tomonan yuzaga ltrlagan aust hosalar.3 Tovush to lqn mayona ltronlar qayta taqsmlansh.4 Tovushnng yzoltr yarmo tazgchlara tovush yutlshnng Uayt nazaryas.5 Tovushnng tashq ltr mayona uchaysh 3 I bob bo ycha ulosa 37 II BOB. ULTRATOVUSH TO LQININING NOCHIZIQLI YUTILISHI VA KUCHAYISHI. Eltronlarnng tovush ltron mayona qzsh.boltsmannng nt tnglamas va unng ychm. Ultratovushnng yutlsh (uchaysh otsynt 47 II bob bo ycha ulosa 5 III-BOB. YARIO TKAZGICHLARDA ULTRATOVUSHNING YUTILISHI VA KUCHAYISHI HAQIDA 3. Domy ltr mayon bo lmagana ultratovushnng yutlsh 3. Tashq ltr mayona ultratovushnng uchaysh 6 3.3 Ultratovush uchayshn ω << bo lgana tshrsh 66 III bob bo ycha ulosa 74 Umumy ulosa 76 oyalanlgan aabyotlar 79 4 7 4 38 38 5 5
KIRISH oalara chayotgan ltron jarayonlarn ot,magnt usullar blan o rgansh qanchal ahamyatga ga bo lsa,ularn aust usullar blan taqq qlsh ham shunchal ahamyatga ga bo lgan usullar srasga ra.bu usul hozrg zamon zasnng uchl usullaran br hsoblana va shu bosan ushbu magstrl ssrtatsyas yuqor lamla va ch tv massaga ga bo lgan n InSb turag yarmo tazgchlara ultratovush to lqnnng yutlsh va uchayshga bag shlan. Ushbu magstrl ssrtatsyasa ω >>, ω >>, shartlar >> qanoatlangan vaqta yarmo tazgchlara tarqalayotgan tovush to lqnnng nochzql yutlsh qarab chqlgan.una tovush yutlshnng nochzql bo lshlg,yutlshnng tovush chastotasga bog llg Uayt nazaryasag bog lanshlaran tamoman arq qlshlg o rsatlgan. Shunng,ssrtatsyaa tovush yutlshnng ltronlar sochlsh manzmga ham muhm bog lansha bo lshlg anqlangan. hama yuqorag tngszllar o rnl bo lgana bunay tovushnng tashq ltr mayona uchaysh qaralgan.shu sabab brlgan boba ytarlcha uchsz omy ltr mayona tovushnng uchaysh qarab chql.araz qln,yuqorag tngszllaran tashqar brlgan mayonga ham quyag shartlarnng bajarlsh yulan: Bu yra, E << q, E << ltron uchun aratrl bo lgan nrgya va muls.org tngszllarnng z ma nos shunan borat,tashq ltr mayon tomonan ltronga brlagan uch va muls ltronga os bo lgan uch va mulsan jua ch b hsoblana.boshqacha qlb aytgana,bu tngszllar tashq mayonnng naqaar uchszlgn oa ta.tovushnng brlgan chastotasa unng uchaysh ltronlarnng ry tzlgga bog lq bo lgan uchun ssrtatsyaa ry tzlgnng ulq tshrl.brlgan hola tovush uchaysh ostonasnng ( ( V w shart uchaysh ostonas yla chastotaga bog lqlg tov
hatto chzql hola ham mavju bo lar an.a lum sochlsh manzma bunay bog lansh logarm tus ham olsh mumn bo la. Dssrtatsya mavzusnng asoslansh va unng olzarblg. Yuqora ltrlgan tngszllar bajarluvch yuqor lamla ga bo lgan yarmo tazgchlara ultratovushnng ytlsh nazaryas 4-5 o quv yla nazary za aras qoshag magstraturan tamomlagan B.Tog ayvnng magstrl ssrtatsaysa qarab chqlgan.bunay sharota ultratovushnng uchaysh nazaryas ushbu ssrtatsyanng mavzus qlb tanlan,chun yuqorag tngszllar qanoatlanagan hollara tovushnng uchaysh bzgacha o rganlmagan.tanlab olngan mavzunng o lzarblgga lsa,aust zanng asosy masalalaran bo lb,moaa tarqalayotgan tovush to lqnnng yutlsh va uchaysh hsoblana,chun bu masalalarn o rgansh orqal tshrlayotgan moalara chayotgan lctron jarayonlar,bu jarayonlarnng ltronlar sochlsh manzmlarga bog lq bo lsh orqal o gna narsalarn blb olsh mumn bo la. Taqqot maqsa va vazalar: Ishnng maqsa: nazaryaan ma lum,tovushnng yarmo tazgchlara yutlsh (uchaysh Uayt ormulasa turuvch w V haga bog lq bo la.agar tovush tzlg ( s w s ltronlarnng ry tzlg V an tta bo lsa,tovushnng yutlsh,asncha bo lsa,tovushnng uchaysh yuzaga la.bz o rgangan masalaa tovushnng chastotas olnan brlgan bo la,qaralgan masalamznng ancha muraablg nuqta nazaran,bz aqat ry tzlgnng yuqora qay qlngan tngzzllara ulqnng qanay o zgarsh ahamyatl bo lganan bz ana shu ry tzlgn turl chgaralar va sochlsh manzmlarag ulq o rganl. Brlgan ssrtatsyaa nch br masala ham o rganl. Yuqor lamla ga bo lgan yarmo tazgchlara to lqn uzunlg uson uzunlan ancha ch,ln ltronlarnng rn chosh uzunlgan ancha atta bo lgan ultratovushnng yutlsh va uchaysh qarab chql.chastotalarnng bu sohasa tovush yutlsh otsyntnng chastotaga bog lqlg gronam
bog lanshlaran batamom arq qlsh,bunay bog lanshlarnng ustun manzm bo lb muls rlasatsyas hsoblansh anqlangan.sochlshnng ayrm manzmlara yutlsh (uchaysh otsynt chastotanng asrl arajasga roorsonal bo lsh hama uchaysh ostonasga to g r lagan ltr mayonnng chastotaga bog lq bo lshlg o rsatlgan.tashq magnt mayon bo lmagan va mavju bo lgan hollar qarab chql. Ishnng vazalar. Qarab chqlgan masalanng brnch qsma B.Tog ayv ssrtatsyasa ychlgan Boltsman tnglamas ychman oyalanl.bu ychmnng azo va vaqta tz o zgaruvchan qsm orqal turl hollara ry tzlgn anqlash lozm.asalanng nch qsma ω, q D >> << tngszllar qanoatlangan vaqta tovushnng srsya qonunn hsoblash ra bo la. Taqqotnng asosy masalas va arazlar. Qaralgan masalanng brnch qsma ltronlar ry tzlgn hsoblab,.unng tovush chastotasga va ltronlar sochlsh manzmga qanay bog lansha bo lshlgn anqlash masalas tursa,unng nch qsma ultratovushnng yuqor lamla va ch massaga ga bo lgan yarmo tazgchlara anqlash vazas tura.hsoblangan barcha attallar masus nuqtaga ga bo lgan br ntgral orqal amalga oshrla.buna asosy roln ntgral maraja joylashgan o zgaruvchnng arajasa turgan 3 / ± v songa bog lq bo la.asalan qarab chqsha 3 / ± v yo > yo < b araz qlna.agar bu son bo lsa,bz qaraygan ntgral masus nuqtas ayo bo la va masalan ychb bo lmay. avzu bo ycha aabyotlarnng qsqacha tahll. Dssrtatsyaa qarab chqlgan mavzu yarmo tazgchlara ultratovushnng yutlsh va uchaysh umumy mavzusga o bo lb,bu masala yarmo tazgchlara astlab Uayt,Xatson,Gurvch,Pustovoyt,Gulyayv va boshqalar tomonan o tgan asrnng 6-7 yllara qarab chqlgan va bu jarayon turl tomonan o rganlngan.shu sababan bz trgan aabyotlar ro yata ana shu mualllar shlar qay tlgan.bz ssrtatsyaa o rgangan masala otsnt Parayv tomonan uzoq yllar avoma o rganlb lnmoqa va bznng ushbu shmz
ma lum br ma noa shu shlarnng avom hsoblana.bz Parayv O.P. rahbarlga Tog ayv tomonan bajarlgan magstrl ssrtatsyas shn avom tr va tovushnng uchaysh masalasn qarab chq. Taqqota qo llanlgan uslublarnng qsqacha tavslar: Ko rlgan masalanng brnch qsma ω >> bo lganan moaa tarqalayotgan tovush una qo shmcha ltr mayon yuzaga ltra va bu mayona o tazuvchan ltronlarnng qzuv mayonga la-taqsmot unsya nomuvozanat holatga la.holatn nomuvozanatl holga ltragan taqsmot unsyasn n Boltsmannng nt tnglamasn ychsh usul blan toshga to g r la.asalanng nch qsma tovushnng ltronlarga ta sr ularnng onsntratsyasnng o zgarshga olb la.bu attallar o rtasag munosabat ltronlarnng javob unsyas n ( ω ϕ ( ω K ( ω orqal tola b araz q qlna va barcha zlanayotgan aramtrlar ana shu K (ω q -javob unsyas orqal anqlana. Taqqot natjalarnng nazary va amaly ahamyat: Dssrtatsyaa brnch marta ltronlarnng ry tzlgnng tovush chastotasga noanalt bog lansha bo lsh anqlangan.shunng,ltronlarnng sochlsh manzmga muhm bog lqla bo lsh ham anqlangan.bu natjalar nazary yangl hsoblana va tovush uchaysh otsyntnng sochlsh manzmlarga bog lqlgan sochlsh manzmlarn anqlash mon ayo bo la. Taqqotnng lmy yanglg: Dssrtatsyaa qarab chqlgan masala ham lmy jhatan yang natjalar hsoblana va ular muallnng matbuota lon qlngan ta lmy maqolasa o z oalarn toganr. Dssrtatsya tarbnng qsqacha tavs: Dssrtatsya uch boban borat bo lb,unng bob ultratovushnng yarmo tazgchlara chzql va nochzql yutlsh (uchaysh ga bag shlanganr.dssrtatsyanng uchnch bob una qarab chqlgan masalalar va ularnng nazary ychmlarga bag shlangan. Nazary za aras qoshag magstraturan 4-5 o quv yla btrb q q
chqqan Tog ayv B. nng magstrl ssrtatsyasa ω >>, ω >>, >> shartlar qanoatlangan vaqta yarmo tazgchlara tarqalayotgan tovush to lqnnng nochzql yutlsh qarab chqlgan.una tovush yutlshnng nochzql bo lshlg,yutlshnng tovush chastotasga bog llg Uayt nazaryasag bog lanshlaran tamoman arq qlshlg o rsatlgan. Shunng,bu sha tovush yutlshnng ltronlar sochlsh manzmga ham muhm bog lansha bo lshlg anqlangan.ln vaqt ytshmaganan Tog ayv tomonan yuqorag tngszllar o rnl bo lgana bunay tovushnng tashq ltr mayona uchaysh qaralmagan.shu sabab brlgan boba ytarlcha uchsz omy ltr mayona tovushnng uchaysh qarab chql.araz qln,yuqorag tngszllaran tashqar brlgan mayonga ham quyag shartlarnng bajarlsh yulan: Bu yra, E << q, E << ltron uchun aratrl bo lgan nrgya va muls.org tngszllarnng z ma nos shunan borat,tashq ltr mayon tomonan ltronga brlagan uch va muls ltronga os bo lgan uch va mulsan jua ch b hsoblana.boshqacha qlb aytgana,bu tngszllar tashq mayonnng naqaar uchszlgn oa ta.tovushnng brlgan chastotasa unng uchaysh ltronlarnng ry tzlgga bog lq bo lgan uchun ssrtatsyaa ry tzlgnng ulq tshrl.brlgan hola tovush uchaysh ostonasnng ( ( V w shart uchaysh ostonas yla chastotaga bog lqlg tov hatto chzql hola ham mavju bo lar an.a lum sochlsh manzma bunay bog lansh logarm tus ham olsh mumn bo la. Dssrtatsyanng bu qsma olngan ana Sunay natjalar Toshnta 5 yl 3-4 otabrlara bo lb o tgan «Nazary va yaro zasnng olzarb masalalar» mavzusa bo lb o tgan lmy onrnsya matrallarnng 47-5 btlara cho tlgan. Dssrtatsyanng brlgan boba shunng yuqor lamla ga bo lgan yarmo tazgchlara to lqn uzunlg uson uzunlan ancha ch,ln ltronlarnng rn chosh uzunlgan ancha atta bo lgan ultratovushnng
yutlsh va uchaysh qarab chqlgan.chastotalarnng bu sohasa tovush yutlsh otsyntnng chastotaga bog lqlg gronam bog lanshlaran batamom arq qlsh,bunay bog lanshlarnng ustun manzm bo lb muls rlasatsyas hsoblansh anqlangan.sochlshnng ayrm manzmlara yutlsh (uchaysh otsynt chastotanng asrl arajasga roorsonal bo lsh hama uchaysh ostonasga to g r lagan ltr mayonnng chastotaga bog lq bo lshlg o rsatlgan.tashq magnt mayon bo lmagan va mavju bo lgan hollar ham qarab chqlgan.
I BOB. PYEZOELEKTRIK YARIO TKAZGICHLARDA ULTRATOVUSHNING TARQALISHI.. Pyzoltr rstallara ultratovushnng ltronlar blan o zaro ta sr Pyzoltrlar shunay rstallar, ulara br jnsl ormatsya ta sr osta bu ormatsyaga roorsonal bo lgan ltr mayon hosl bo la. Krstallnng yzoltr ususyat unng smmtryas blan chambarchas bog langan. Pyzoltr samara Cs, ZnO, GaAs, InSb, T ab o gna rstallara uzatla [,]. Agar yzoltr avry last to lqn-ormatsya to lqn tarqalayotgan bo lsa, bu to lqnnng azovy va vaqt bo ycha avrylgga ga bo lgan ltr mayonlar hosl qla. Aytsh mumn, har qanay last to lqn a b c -rasm. Yass onl anjara: a - smmtrya marazga ga bo lmagan anjara; b - ormatsyalanmagan yachya; c - strla yo nalsha cho zlgan yachya;
bunay rstallara bo ylama ltr mayon to lqnn yuzaga ltra (bunan yn bu mayonn yzoltr mayon b ataymz. En bz yzoltr samaranng yzoltrlara tarqalayotgan tovush to lqnga qanay ta sr tshn qarab chqayl. Dormatsya ta sra bunay rstallara yzoltr mayon hosl bo lgan uchun uchlansh tnzor oasa bu mayonga roorsonal bo lgan qo shmcha ha ayo bo la. Bunan tashqar ormatsya vaqta rstalla ayo bo lagan qutblansh ltr nutsyasga qo shmcha tuzatma rtla. Pyzoltrlara uchlansh tnzornng ochq o rnshn atarayl. Bunng uchun ormatsyaga lgan yzoltrnng ozo nrgyasn qaraymz. Bu nrgyanng Ф b blglasa, unng oasa ormatsya tnzor haan tashqar U l U nng varatga roorsonal bo lgan E o aytmaga roorsonal bo lgan halar ham shtro ta. Bz qaralayotgan yaqnlashuva ozo nrgyanng umumy o rnsh quyagcha bo la: 8π Ф Ф clmu Ulm EE β, leu l (.. bu yra ltr sngruvchanl tnzor, β, l - yzoltr moullarnng uchnch rang tnzor, Ф ormatsyalanmagan holat ozo nrgyas. Umumy qabul qlngan qoaga o ra, uchlansh tnzor ltr nutsya sa Ф σ clmu lm βl, El, E cojnst U (.. Ф U (..3 D 4π U const E 4πβ, l E Shunng uchun yzoltrlara tovushnng tarqalsh tnglamas u U m E ρ c,, lm βl (..4 t o rnsha yozla. Bzng rstallmz yzoltr bo lsa, ltronamaag Puasson tnglamas v D, l
qaralayotgan hola sa E ul 4 πβ, l (..5 o rnshn ola. (..4, (..5 tnglamaag u va ϕ ltr otntsaln ( E graϕ -n slang! u u [ ( r ω ], t ϕ ϕ [ ( r ω ] t o rnsha avry o zgara b hsoblasa, quyag algbra tnglaman olamz: ρω u c u β ϕ, (..6 lm l m l, ϕ 4 πβ, u (..7 l l l Bu tnglamalaran ϕ n yo qotb, quyag srsya tnglamasga ga bo lamz: bu yra ( β ( l, mlm β, q q ρω δ clmlm 4π, (..8 rs r s, δ - Kronr blgs., ω Ko rna, yzoltrlara (..8 trmnant nsbatnng brnch tartbl br jnsl unsyas hsoblana va srsya qonun ω w o rnsha brla, bu yrag tzl w -nng yo nalshga muraab bog lansha bo la. Dtrmnantag yzoltr tuzatman lastl moullar tnzorga qo shlagan tuzatma tarqasa ham oalasa bo la: c ' lm c δc, (..9 lm lm bu yra 4 πβl, mβ, qnnq δ clm, n (.. n n rs r s
araz qlayl tovush to lqn n yo nalsh bo ycha tarqalayotgan va qutblansh vtorga ga bo lsn. U hola (..4 haraat tnglamas ' ρω c oy o rnsh ola. Bu yra c nn c c lm n n (..9 ag tuzatma δc -nng c ga nsbat last tbranshlarn ltr mayon blan bog lovch yzoltr omyl b atala: δ c 4πβ n, n β n, n χ(, n. c c Bu omyl qutblanshga va tovush to lqnnng tarqalsh yo nalshga bog lq bo la. (..9 an o rna, yzoltr samara rstall lastl moul mqornng oshshga olb lar an. Shunng uchun tovushnng yzoltra tarqalsh tzlg noyzoltrlarag tzlgga nsbatan attaroq bo la. Pyzoltr rstallarnng o a (yzoltr yarmo tazgchlarnng barchasa oata χ jua ch ( χ << attal hsoblana. Shunng uchun yzoltr yarmo tazgchlar aust ossalar nazaryasa bu attaln nn l nn nazaryanng ch aramtr b tanlab olna [3]. Pyzoltr tnzor m β, l haqa og z so z. Bu tnzor l jut nslar bo ycha smmtr tnzor hsoblana, u ma lum br smmtryaga ga bo lgan rstallara nolan arql qymatga ga bo la. asalan, maraz smmtryasga ga bo lgan rstallara toq rangag barcha tnzorlar nolga tng bo la... Eltronlar tomonan yuzaga ltrlagan aust hosalar Yarmo tazgchlar ltrlaran shu blan arq qla, chl tmraturaa yarmo tazgchlara ma lum mqora rn zarya tashuvchlar mavju bo la. Yarmo tazgchlara uzatlagan aust samaralarnng o zga os ususyatlar tovush to lqnnng ana shu zarya tashuvchlar blan o zaro ta srga asoslanganr. Albatta bunay samaralar rstall anjaralar tomonan
ham chaqrlsh mumn. Bu turag samaralar tovush to lqnnng anjaras ssql tbranshlar, ularag nuqsonlar va hoazolar blan o zaro ta srga asoslangan bo la. Ln yarmo tazgchlarag anjaravy samaralar ltrlara uzatlagan ana shunay samaralaran yarl arq qlmagan uchun bz asosy tbormzn rn zarya tashuvchlar - ltronlar blan bo lgan aust samaralarga qaratamz. Tovush to lqnnng o tazuvchanl ltronlar blan o zaro ta srnng qanay amalga oshrlshn qarab chqayl. Bz o rgan tovush to lqn rstallag hosl bo lagan avry ormatsya to lqn b hsoblana. Krstall ormatsyas unng zonalar struturasnng o zgarshga olb la. Natjaa ormatsya vaqta vazmulsga ga bo lgan ltron nrgyas o zgara. Dormatsya ch bo lgana, taby, bunay o zgarsh ham ch bo la va aytsh mumn u ormatsya tnzor U -ga roorsonal bo la. Shunay qlb, ormatsyalangan rstalla ltron nrgyasn ( ( Λ U tarqasa oalasa bo la. Bu yra ( ormatsyalanmagan rstalla ltron nrgyas, Λ nch rang tnzor bo lb, ormatsya vaqta ltron nrgyasnng o zgarshn oalay. Dormatsya tnzor o lchaml attal bo lganan Λ nrgya o lchamga va atom nrgyas tartbag qymatga ga bo la. Shunng uchun tartb brga tng bo lgan ormatsya ayta ltron nrgyas o znng attalg tartba o zgarmog lozm bo la. Λ tnzor omonntalarnng aratrl qymat br ncha ltron volt atroa bo la. Bu tnzor ormatson otntsal tnzor yla. Umuman aytgana ltron vazmuls ga bog lq bo la. Λ tnzor Ln yarmo tazgchlara bu bog lansh muhm ahamyatga ga mas, chun ulara rn ltronlar mtallaragga nsbatan ancha am mqora bo la va ular zonalar strmumlar yaqnag azonng ozgna qsma taqsmlangan bo la. Λ o zgarshnng aratrl masshtab Brllyun zonas
chgaravy vazmuls tartba, ya n a h tartba bo la (a - rstall anjara omys, h - Plan omys. Shunng uchun zonalar strmum yaqna qatorga yoyb, qatornng brnch ha Λ n Λ const blan chgaralansa bo la. tallara bunay yaqnlashuv noo rn bo la, chun ulara Λ Λ ( bog lansh muhm hsoblana. Dormatson o zaro ta sr barcha yarmo tazgchlara mavju bo la. Ln u o zaro ta srnng yagona manba s bo lb hsoblanmay. Bunan tashqar, yzoltr ossaga ga bo lgan yarmo tazgchlarnng ormatsya ayta yuzaga lagan yzoltr mayonlar blan o zaro ta sr ormatson o zaro ta srga nsbatan muhmroq hsoblana. Krsha qay qlganmz, yzoltr yarmo tazgchlara 5 Gts chastotaa austoltron o zaro ta sr noyzoltr yarmo tazgch (masalan, G a hosl bo lagan 5 austoltron o zaro ta sran tartba uchlroq namoyon bo la. Eltronlar tomonan yuzaga ltrlagan aust hosalar cha brnch navbata tovushnng yutlshn slatb o tamz. Bu hosan uzatsh bunchal ham oson mas, chun tajrbaa ltron tomonan tovushnng yutlshn anjara tomonan bo lagan yutlshan arq qlsh oson bo lmay. Ularn br bran arq qlsh maqsaa otoo tazuvchan yarmo tazgchlaran oyalanla, chun ulara yorug l ntnsvlgn oshrsh yorama o tazuvchan ltronlar ontsntratsyasn o aytrsh mon mavju bo la. Boshqa l yarmo tazgchlara sa ltron tomonan bo lagan yutlshn ayrm tshrsh uchun o tazgchn tashq ltr va magnt mayonlarga rtb, yutlshnng o zgarshn o rgansh mumn bo la. Chun bu mayonlar tovushnng anjaravy yutlshn o zgarmasan ltronl yutlshga uchl ta sr o rsata. Klgusa bz aqat ltronl yarmo tazgchlarag aust hosalarn qaraymz (oval yarmo tazgchag aust samaralar ltronl samaralarga o shash bo la. Bzn qzqtragan ltron ontsntratsyalar 6 3 sm atroag qymatlarga ga bo la.
O tazuvchan ltronlar blan bog lq bo lgan navbatag aust samara tovush tzlgnng bz tshrayotgan yarmo tazgchlara o zgarshr. Oata bunay o zgarsh o tazuvchan ltronlar ontsntratsyas o zgarsa yo magnt mayon uchlanganlg o zgargana ro yobga lsh mumn. Nhoyat, bz qaraygan uchnch aust t o tazgcha austoltr tonng hosl bo lsh va natjaa o tazgch solshtrma qarshlgnng o zgarshr. Oata org t ltrlara uzatlmay [3-4]..3.Tovush to lqn mayona ltronlar qayta taqsmlansh Yarmo tazgchlara yzoltr mayon blan o tazuvchanl ltronlarnng qanay o zaro ta sr qlshn qarab chqayl. araz qlayl, astlab qanayr vaqt momnta o tazgcha azovy avry stat ormatsya u u cos yaratlgan bo lsn. Qulayl uchun o q rstall smmtrya o q bo ylab yo nalsn, u vtor sa ga aralll bo lsn. Bu hola β, j tnzornng aqatgna btta omonntas muhm hsoblana va bu omonntas salyar attal bo lb, un β orqal blglayl. Klgusa ana shu holn qaraymz va barcha joya β salyar attal b hsoblaymz. Pyzoltr uchun Puasson tnglamas an u E 4πβ E 4πβ u (.3. tngla ga bo lamz. E ϕ bo lgan uchun
anlg lb chqa. 4πβ ϕ u (.3. Pyzoltr o rna yzoltr yarmo tazgch bo lsa, o tazuvchan ltronlar hulq qanay bo la? Bu hola tovush yaratgan yzoltr mayona ltronlar azoa qayta taqsmlana, ular otntsal cho qqlaran tushb, otntsal «o ra»larn to lrshga haraat qla. Bunng natjasa boshlang ch otntsal ϕ amaya yo boshqacha qlb aytgana bu otntsalnng o tazuvchan ltronlar tomonan to slsh yuzaga la. Shunng uchun bz brnch savol, u ham bo lsa, ltronlarnng qayta taqsmlansh qanay sor bo la va qanay qlb otntsal ltronlar tomonan to sla, gan savolga javob toshmzga to g r la. Bunng uchun bz ltronnng tovush to lqn mayona qanay haraat qlshn anqlashmzga to g r la. Bu masalanng ychm tovush to lqn uzunlg π va ltronlar rn chosh yo l uzunlg l o rtasag munosabatga, yo l aramtrnng attalgga jua bog lq bo la. Bu aramtr umuman o tazgchlar aust ossalar nazaryasa muhm aramtr hsoblana, unng turl qymatlara ltronlar tovush blan turlcha o zaro ta sr qlsha. Bz bu bo lma uzun to lqnlar aazonn qaramoqch bo lganmz uchun hol blan chgaralanamz. l << ( l << λ Bu shart shun o rsata,tovush to lqn uzunlg tartbag masoalara ltronlar jua o marta o zaro to qnashb ulgura. Bunay to qnashuvlar natjasa ltronlar taqsmota muvozanat holat hosl bo la - ltronlarga ltr o tazuvchanl σ va uzya otsnt D blan haraatlanuvch hajmy zarya tarqasa qarash mumn bo la. Natjaa to zchlgn j δn σ E D (.3.3
o rnsha yozshmz mumn. Bu yra δ n ltronlar ontsntratsyasnng o zgarsh ( δ n n n, - ltron zarya. (.3.3 nng brnch ha oy Om qonun blan oananuvch to, nchs azoa ltronlarnng br jnsl bo lmagan taqsmot tuayl yuzaga lgan uzon tor. Tashq ltr mayon bo lmagana statsonar holata to zchlg bo lmog zarur. Shunng uchun bunay holata (.3.3 an σ δn ϕ D j nolga tng Bu yra bz yzoltr mayon E n ϕ orqal oala: ϕ E Yarmo tazgch hola Puasson tnglamas o rnsha yozlgan va nutsya D 4πδ n bo lgan uchun Puasson tnglamas n ϕ u D 4πβ ϕ 4πσ u ϕ 4πβ (.3.4 D o rnshn ola. Dormatsya bo lmagan vaqta (.3.4 ϕ va bu yra ϕ 4πσ D ϕ hoslanng o lcham R ϕ (R-uzunl o lcham bo lganan otntsal ϕ nng azovy o zgarshn anqlovch aratrl uzunl bo lb,
D 4πσ R (.3.5 attal hsoblana. uvozanat holata ltr o tazuvchanl σ, uzya otsnt D o zaro Eynshtyn munosabat b ataluvch munosabat blan bog langan bo la. Bu munosabat muvozanat holata to lq tonng mavju bo lmaslg talaban lb chqa. uvozanat holata ltronlar ontsntratsyas n nng aqat myovy otntsal ζ ga bog lq bo lgan uchun (.3.3 tngl o rnshn ola. uvozanat holata ltromyovy otntsal qymatga ga bo lshlgan [6], ζ ϕ tngla ga bo lamz va j bo lganan (.3.6 an j ϕ n ζ σ ( D ζ (.3.6 ζ ϕ omy σ n D (.3.7 ζ (muvozanat holata n n. (.3.7 n (.3.5 ga qo yamz: R 4π n ζ (.3.8 Boltsman statstas hola n n ζ T ( - Boltsman omysn bunan yn b olamz bo lgan uchun
R T (.3.9 4π n bo la va u Dbay-Xyul to slsh raus yla. rm statstas hola va n 3n ζ ζ R ζ (.3. 6π n Tomas - rm to slsh raus yla. Bz qarayotgan hola ϕ, u cos qonun blan o zgarayotgan uchun (.3.4 tnglamanng ychm yo ϕ ϕ R ϕ ( R ( R ϕ ϕ (.3. o rnsha brla va bu yra ϕ (.3. ormula blan anqlana. Shunay qlb, yzoltr otnsalnng ltronlar tomonan to slsh tovush to lqn π uzunlg va to slsh raus R lar o rtasag munosabatga bog lq bo lar an. Agar R<< (ya n R << λ bo lsa, φ << φ bo la-yzoltr otntsal to lq to slb qolna, ya n o tazgchnng yzoltr ossas yo qola va u o zn yzoltr ltr ab hs ta. Asncha, R>> bo lsa, ltronlarnng azoag qayta taqsmlansh qsqa to lqnl tovushn szmay. (.3. munosabatn yana quyagcha ham tushnsh mumn: statsonar holata mayon tomonan yuzaga ltrlgan o tazuvchanl to blan azoa
ltronlarnng qayta taqsmlansh tuayl hosl bo lgan uzon tonng muvozanat mavju bo la. Shunng uchun ltr o tazuvchanlnng uzya otsntga nsbat qancha atta bo lsa, ltronlarnng qayta taqsmlansh shuncha o bo la yo brlgan nng qymata R shuncha ch bo la. Boshqacha qlb aytgana azoa qancha o ltronlar qayta taqsmlansa, boshlang ch otntsal φ nng to slsh shuncha samaral bo la. T hollara to slsh rausnng aratrl qymatlarn ltramz. CS rstala uy tmraturasa T 4 rg, n sm -3 bo lgana 5 4 4 3 5 R sm; n sm a R sm ( 9,4 5 araz qlayl, n rstalla tarqalayotgan tovush to lqn rstallnng har br nuqtasa ω chastota blan avry o zgaruvch ltr mayon yaratayotgan bo lsn. Savol tug la: yuqora bayon tlgan stat to slsh qanay vaqt cha amalga osha? Bu savoln oynlashtrsh uchun nostatsonar holata to zchlg omy bo la olmaslgn va unng oornataga bog lq bo lshlgn hsobga olamz. Oata bunay bog lansh uzluszl tnglamas δn t vj blan anqlana [5]. Bu tnglama blamz, ltr zaryanng saqlansh qonun hsoblana. Bu tnglamaag j o rnga (.3.3 tnglamaag qymatn qo yb, barcha o zgaruvch attallarn azovy bog lansh [] qonun blan brlshn slasa, δn t D δn σ ϕ tnglamaga ga bo lamz. (.3. ag δ n o rnga Puasson tnglamas ag ϕ ϕ 4πδn δ n qymatn qo ysh natjasa toamz: (.3.
ϕ ω ( R ϕ ( R ω (.3.3 Agar R<< b olsa, ltronlarnng muvozanat quyqasnng aratrl rlasatsya vaqt bo lb (.3.4 4πσ hsoblana va u masvllcha rlasatsya vaqt yla. (.3.4 an o rna, ltr o tazuvchanl σ ga tsar roorsonal bo la, chun ltr o tazuvchanl jarayonlar tuayl o tazuvchanl ltronlar azoa qayta taqsmlana ola. Agar ω attal ch bo lsa, tovush avr cha stat to slsh to la amalga osha hama ltronlarnng azoag taqsmlansh manzaras stat holag taqsmlanshan yarl arq qlmay. Bu hola φ otnsal φ an ( R ( R o ayuvch blan arq qla. Xu ana shunay o ayuvch yzoltr t tuayl yarmo tazgcha tarqalayotgan tovush tzlga ham shtro ta: w χ ( R ( R w Tsar chgaravy hola ya n ω >> bo lgana, to slsh hosl bo lb ulgurmay va yzoltr yarmo tazgcha tovush tzlg unng yzoltrag tzlg w ga tng bo la: χ w w w Chastotalarnng ng ntrvala tovush tzlg
w w χ ( R [ ( R ] ( ω [ ] ( R ( ω oa blan anqlana. Yarmo tazgchag ltronlarnng una tarqalayotgan tovush to lqnga javobn sat jhatan qarab chqqanmzan yn n bz tovushnng yutlsh va uchayshn hsoblashga rshamz..4.tovushnng yzoltr yarmo tazgchlara tovush yutlshnng Uayt nazaryas Qulayl uchun yzoltr yarmo tazgcha toza aust (o nalang yo bo ylama to lqn tarqalayotgan bo lsn. Sljsh omonntasn u, lastl moullar tnzorn oy c, yzoltr moullar tnzorn oy β orqal blglayl. U hola tarqalayotgan tovush to lqn lastl nazaryas tnglamas Puasson tnglamas u t u c ρ E β, (.4. uzluszl tnglamas u E πβ 4π n δ 4, (.4. δn j t (.4.3 ab tnglamalar sstmas blan tavslana. Albatta, bu tnglamalar sstmasga o tazuvchanl to zchlg j δn σ E D (.4.4
tnglamasn qo shsh ra bo la. Agar bz ϕ E anlgn va (.4.-.4.4 tnglamalar sstmasag ϕ u, δn, larn [ ( ωt ] qonun blan o zgara sa, (.4.-.4.4 lar o rna bz quyag tnglamalarga ga bo lamz: ( c ρω u β ϕ 4πβ u ϕ 4πδn σ ϕ [ D ω] δn (.4.5 Olng mavzulara o rganmz (.4.5 tnglamalar sstmas ychm bu sstma otsntlaran tashl togan trmnantnng ga tng bo lgana mavju bo la. Bu sa tovush to lqnnng yzoltr yarmo tazgchlarag srsya qonun ω ( n anqlay. Dsrsya qonunn toshnng osonroq yo l (.4.5 tnglamalarag org tnglamaan δn ( R ( ω D (.4.6 ϕ n toshr. Agar va R attallar orqal (.4.6 n yozsa, δ n quyagcha yozla: δn ( R n ϕ ( R ω ζ Org tngln (.4.5 tnglamalarnng nch tnglamasga qo yamz Bu tnglama (.4.5 nng brnch tnglamas blan brgala (.4.7 4πβ ( R ω u ϕ ( R ω br jnsl chzql tnglamalar sstmasn tashl ta [5-7]. Ularan (.4.8 u, ϕ larga nsbatan
4πβ β c ( R ω ( R ω ω ρ bo lshlgn toamz. Bu yra ω - yzoltr bo lmagan w c ltra tovush to lqn vtor attalg. Org trmnantn ochb yozamz: ( [ ( R ω ] χ ( R ω (.4.9 4πβ Bu yra χ bzga olng mavzularan tansh bo lgan yzoltr c bog lansh otsynt. araz qlayl, astlab χ bo lsn. U vaqta (9 ta o zaro bog lq bo lmagan tnglamaga ajrala:, ± bu o q bo ycha tarqalayotgan oy tovush to lqnr; ( R ω yo ± ω R bu sa uchl yutlayotgan to lqnr, chun ( R ω En bzag otsynt χ bo lsn. Bu hola bz qarayotgan man va ltron sstmalar o zaro ta srlanuvch sstmalar hsoblana. Tovush to lqnlar uchun χ<< bo lgana srson tnglama (.4.9 nng ychmn toamz. Krstall chgarasa ω chastota blan tbranayotgan sljsh brlgan b, (.4.9 tnglamaan (ω bog lanshn atarayl. asalanng bunay qo ylsha (ω to lqn vtor omls attal hsoblana. Unng haqqy qsm, ya n R(ω
tovush aza tzlgnng o zgarshn, mavhum qsm Im(ω sa tovush to lqn amltuasnng susayshn oa ta. Haqqatan, [ ωt R ( ω ] ( ω t Im Tovushnng yutlsh otsynt G b, oata, S ln attala aytla, bu yra S - tovush amltuas varatga roortsal bo lb, unng ntnsvlgn blra. Shunng uchun G Im (.4. orqal tola. χ<< bo lgan sababl ( b hsoblash mumn bo la, natjaa (9 nng [..] qavs cha joylashgan oasa b yozsh mumn va (.4.9 o rnga o bo ycha brnch yaqnlashuva o ( R ω χ ( ( R ω (.4. yozsa bo la. Bu nsbatnng mavhum qsmn ajratb olamz [9]. Bunng uchun: R ω ( ( R ω ( ( ω ( ( R ω ( ( R ω ( ( R ( ω va unan G R ω R ω Im χ (.4. ( ( R ( ω
Bu ormula Uayt tomonan chqarlgan bo lb, yzoltr yarmo tazgcha tovushnng yutlsh chzql otsyntn oalay.tovush tzlgnng o zgarsh sa χ R ( R ( ω w ω, (.4.3 ( R ( ω bu yra w w w. Yutlsh otsyntnng chastotaga (.4. ormula blan bog lansha bo lshlgn quyagcha tushuntrsa bo la. Pyzoltr mayon tomonan yuzaga ltrluvch o zgaruvchan to rn zaryalarn qayta taqsmlanshga olb la. Bunay zaryalar o z navbata qo shmcha ltr mayonn hosl qla. Bu mayon astlab ltr mayonga nsbatan tsar yo nalgan bo la va natjaa o tazuvchanl tonng amaysh uzatla. asvlcha rlasatsya vaqt shunay vaqt, unng avoma zaryalar qayta taqsmlana. Stat ormatsya vaqta qayta taqsmlangan zaryalar mayon to slgan yzoltr mayon tomonan shunay omnsatsyalana, ltr to nolga tng bo la. Agar ormatsya ω << chastota blan o zgarsa, tonng yarl to lq omnsatsyas sor bo la. To g rrog, o zgaruvchan ormatsyaa hajmy zaryalar mayon stat ormatsya vaqtag mayonan ω ga roorsonal bo lgan jua ch attala arq qla. Shunng uchun yzoltra ω ga roorsonal bo lgan o zgaruvchan to oqayotgan bo la. Yutlsh otsynt to zchlgnng varat blan anqlanganlg sababl ω ga roorsonal bo la. Tsar chgaravy hola, ya n ω >> bo lgana, tovush avrga tng vaqt cha hajmy zaryalar mayon hosl bo lb ulgurmay [8]. Shunng uchun brlgan hola to zchlg va ltr mayon o rtasag otsnt chastotaga bog lq bo lmay. Shu sababl α ham ω ga bog lq bo lmay. (.4. oanng marajag ( ω ha br holan nch br holga chgaravy o tshn ta mnlay.
Nhoyat, R >> bo lgana yutlsh otsynt ω nng oshsh blan tz amayb bora. Bu hola to lqn uzunlg to slsh rausan jua ch bo lgan tovush to lqnlar hatto stat hola ham zaryanng qayta taqsmlanshga olb la olmaganlg sababl shunay hosa uzatla. Yutlsh otsynt chastotanng ω m qymata o znng masmal qymatga rsha, ya n tovush to lqnnng λπr qymata G ma w R χ 4R
.5.Tovushnng tashq ltr mayona uchaysh omy araz qlayl, tovush to lqn tarqalayotgan yzoyarmo tazgch ltr to oqayotgan zanjrga ulangan bo lsn. Unan o tayotgan to orqal tola. Bu yra j nυ (.5. j υ E const n ltronnng ry tzlg b aytla. Agar omy ltr mayon uchsz bo lsa, zanjra hosl bo lagan to ltr uchlanganl E blan Om qonun j σ E (.5. bo ycha bog langan bo la []. Boltsman statstas hola o tazuvchanl ltron ontsntratsya n ga roorsonal bo lganan ry tzlg ormula blan anqlana. Bu yra υ µe (.5.3 σ µ ltronlar lamlg yla. Ral n sharotlara qqatga sazovor samaralar uchl ltr mayona yuzaga la. Bunay mayonlara n Om qonun amal qlmay qo ya va υ uchun (.5.3 tngl bajarlmay hama Tovush yaratgan ltr mayon υ nng E ga bog lansh ancha muraab bo la. δ E n tashq E mayonga nsbatan jua ch b araz tb, toa tolagan o zgaruvchan qo shmcha δ j uchun δn δ j υδn σe D (.5.4 tngln yozamz. Bu yra σ - rntsal o tazuvchanl va u σ j E E E
orqal tola. Drntsal o tazuvchanlnng zavy ma nos quyagan borat. O tazgch-rsstallnng VAX (volt-amr aratrstasn qarayl. VAX tonng E ga bog lanshn, ya n j(e unsyasn oalay [-]. Oata o tazuvchanl j E nsbat blan, ya n VAX orasnng og mas (- rasma untr blan o rsatlgan blan anqlansa, rntsal o tazuvchanl VAXga o tazlgan urnmanng og mas blan anqlana. Om qonun amal qlgana oy va rntsal o tazuvchanllar br bran arq qlmay, Om qonun o rnl bo lmagana sa ular tuban arq qlsha. j E E -rasm. Nusanng volt-amr aratrstas En tashq ltr mayonnng yutlsh otsntga qanay ta sr qlshn qarayl. Agar bz µ E υ η w w (.5.5 otsntn rtsa, o rsatsh mumn, tovushnng yutlsh otsnta shtro tagan ω bu hola ω almashtrshn o tazshga to g r la va ω η ω η G χ (.5.6 ( R ( ω η
Agar tashq mayonnng brlgan qymata υ bo lsa, η < bo la w va tovushnng moaag oy yutlsh sor bo la. Bu hola ry ltronlar (7-rasm tovushan aza jhatan orqaa qola va tovush yaratgan otnsal < w υ v w w v w v a b v 3-rasm. a w > υ hol; b w υ hol; v w < υ hol. chuqurlnng ront orqasa to lanb haraat qla, natjaa tovushnng susaysh mayonga la.(3-rasm a-hol; υ w bo lgan hola ular br l azaa va br yo nalsha haraat qla, natjaa tovushnng yutlsh yo qola (b-hol, w υ hola sa (v-hol ltron quyqalar tovush to lqnn quvb o tuvch aza blan haraat qlb, o z nrgyasn tovush to lqnga bra va natjaa tovushnng uchaysh yuzaga la. Bu hola υ η < w bo la va yutlsh otsynt o z shorasn o zgartra. Tovushnng ntnsvlg G I I I G qonun blan oshb ta. asalan, CS msola qarayl. Tashq ltr mayon shunay qymatga ga bo lsnm, una
η,44 ω ya n υ w w ( η, 5 bo lgana masmal uchaysh otsynt G ma 8 sm bo la va CS an yasalgan lastna uzunlg 5 sm bo lgana tovush ntnsvlg 4 [ G ] [ 8*5] ma marta oshb ta. Albatta υ, w hosl qlsh uchun ltronlar lamlg 5 sm µ, ltr mayon uchlanganlg s V E 3, bo lmog ra. Agar sm chastotalar yanaa yuqor bo lsa ntnsvlnng yanaa oshb borsh utla. Ultratovush uchayshn tshrsh uchun yasalgan srmntal qurlma smas 3-rasma brlgan. Bu rasmag o zgartgchlar ultratovush to lqnlarn gnratsya va qay qlagan yzoltr lastnalaran yasala. Ularnng qrralarga mtall yoshtrlgan bo lb, ularga lastna ususy tbransh chastotasga tng bo lgan chastotaag o zgaruvchan uchlansh brla va lastnaa tsar yzoltr samara tuayl man tbranshlar yuzaga ltrla, qays u o z navbata ultratovush manba s bo lb zmat qla. Pyzoltr yarmo tazgch CS an yasalgan lastna qrralarga E mayon yaratuvch omy uchlansh brla. CS rstal otoo tazuvchan yzoltr yarmo tazgch bo lganan bu rstalln yortagan nur ntnsvlgn o zgartrsh blan bu rstallnng ltr o tazuvchanlgn ng aazona o zgartrb, unng (ya n nng tovush to lqnnng yutlsh va uchayshga ta srn o rgansh mumn bo la. To lqnnng uchaysh otsntnng ry tzlgga bog lqlg bu tajrbaa o rganlgan. Agar υ, ya n ltronlar ry tzlg tovushnng tarqalsh yo nalsh bo ycha yo nalgan bo lsa, υ bo lgana η bo la va yutlsh otsynt o znng shorasn w
o zgartra, yutlsh uchayshga almasha. Kuchaysh otsyntnng υ ga bog lansh grlg (4-rasman o rna, bu grl, υ w chzqqa nsbatan asmmtr hsoblana. Agar tovush υ > w hola υ ga qarama-qarsh yo nalgan bo lsa, u albatta susaya. Ln bunay hollara G yutl < G uchay bo la. Dry tzlgnng omy qymata uchaysh otsynt o znng masmal qymatga, tovushnng yutlsha uzatlgan ab, ω ωm qymata rsha [5]. Chastota va ry tzlgnng o zgarshga nsbatan uchaysh otsyntnng mutlaq masmal qymat quyagcha bo la: G ma χ 4R G w G anj υ υ υ 4-rasm: Tovush yutlsh otsntnng ry tzlgan bog lansh Hozrgacha bz rstallnng anjara tomonan yuzaga lagan yutlshn hsobga olma. Oata garmon yaqnlashuva tovush anjaranng ssql tbranshlar blan o zaro ta sra bo lmay, tbransh angarmon bo lgan uchun bunay o zaro ta sr mavju bo la. Tovush to lqn hosl qlgan ormatsya ssql tbranshlar vantlar bo lgan ononlar taqsmotnng o zgarshga olb
la. Dormatsya vaqt bo ycha o zgarb turgan uchun bu taqsmot muvozanat bo lmay qola. Bu muvozanatszlnng arajas sa chastota va nomuvozanat ononlar rlasatsya vaqt o rtasag munosabatga bog lq bo la. Ana shunay muvozanatszl natjasa qaytmas jarayon yuzaga la, ya n to lqn nrgyasnng ononlarga brlsh natjasa tovushnng yutlsh yuzaga la. Tovushnng rstall anjaras tomonan yutlsh zavy jhatan aloha tborga loyq masala hsoblana. Ln bzn bunay masala qzqtrmagan uchun unga tbor qaratmaymz. asala shuna, anjara tomonan bo lagan yutlsh u ltrlara sor bo lagan yutlshga o shay, bz sa o tazuvchan ltronlar blan tovush to lqn o rtasa bo lagan o zga os o zaro ta srn o rganayamz. Shunng uchun bz anjara tomonan tovushnng yutlsh otsynt anq va unng qymat brlgan b hsoblaymz. Tovushnng anjara tomonan yutlshn hsobga olgan hola ltron tomonan yutlsh otsyntn qo shsh ra. Shunng uchun yutlsh otsnt uchaysh otsntan atta, anjara yutlsh bo lmagana sa unan ch bo la. Kuchayshnng to lq otsynt ry tzlgnng yagona qymata nolga aylanmasan, unng υ va υ qymatlara nolga aylana. Xatson tomonan tovush to lqnnng qalnlg 7 mm bo lgan CS rstala yutlsh (uchaysh otsntnng tashq ltr mayonan bog lansh bo ycha o tazlgan tajrba natjalarn ltramz (4-rasm. Bu rasma susaysh sanoqnng bosh yorug l blan yortlmagan CS ag susayshga mos la. Yortlsh ntnsvlg o zgargana rsttall o tazuvchanlg, ma, o zgara. Rasmag В, С - grllar ω 45Gts, ω 4, ва 4, 8 qymatlarga mos la. A-grl sa ω5gts, ω,83 qymatlarga tgshl. Rasman ltr mayonnng V E 75 qymata yutlsh otsynt shorasnng sm o zgarganlg o rnb turb-yutlsh uchayshga almasha. Oata nazarya uchaysh otsynt uchun jua atta qymatn bra.
Ayrm tajrba natjalar sa bu otsynt uchun utlgan qymatan am bo lgan natjalarn bra. Bunga asosy sabab shu rsstalla tovushnng uchaysh chsz atta qymatga hch ham ga bo la olmay, chun tovush amltuasnng osha borsh blan nochzql tlar yuzaga la va unay tlar tovushnng uchaysh manzarasn sn o zgartrb yubora. Bz bunay nochzql tlarn ushbu magstrl ssrtatsyasa qarab chqamz.ushbu ssrtatsyanng lgus boba Samarqan avlat unvrsttnng nazary za va vant ltronas aras qoshag nazary za mutaassslgag magstraturan - o quv yla btrb chqqan Haqbryv O tr bajargan magstrl ssrtatsyaa qarab chqlgan nochzql (tovushnng yutlsh va uchaysha tlarn qarab chqamz [-3] va bz qarab chqqan nochzql tlar blan ularn solshtramz.
I bob bo ycha ulosa Brlgan boba yzoltr ossaga ga bo lgan yarmo tazgchlara ultratovush to lqnnng yutlsh va tashq ltr mayona uchayshnng chzql nazaryas qarab chql.brlgan hola tarqalayotgan tovush q l << (bu yra q, l mos ravsha π / q λ to lqn uzunla ga bo lgan tovushnng to lqn vtor va ltronlarnng rn chosh uzunlg shartn 6 8 qanoatlantra.bu tngszl tarqalayotgan tovushnng grts chastotaga ga bo lgan ultratovush bo lshlgn blra.tngszlan o rna,tovushnng to lqn uzunlg ltronlarnng rn chosh uzunlgan ancha atta bo lmog n taqozo ta.dma tovush to lqn uzunlga ltronlar jua o o zaro to qnashb ulgura va shu sababan bunay ltronlarn lctron gaz b hsoblash mumn bo la.bunay ltronlar gaznng tovush to lqn blan o zaro ta srn lass tnglamalar yorama tavslab bo la.shu bosan bu nazaryaa lastl nazaryas tnglamas,puasson tnglamas,ltronlarnng saqlansh tnglamas hama to zchlg uchun tnglamalaran oyalanla va tovush to lqnnng srsya qonun ltrlb chqarla.
II- BOB. ULTRATOVUSH TO LQININING NOCHIZIQLI YUTILISHI VA KUCHAYISHI..Eltronlarnng tovush ltron mayona qzsh.boltsmannng nt tnglamas va unng ychm Tovushnng o zgaruvchan mayona, uchsz ltr mayon E a hama magnt mayon H a joylashgan ltronlar taqsmot unsyas ( ( I H v c E v t (.. nt tnglaman qanoatlantra. Bu yra v, - ltron tzlg va mulsnng omonntalar, - zarya, c -yorug l tzlg. Bu tnglaman Gurvch va Gansvch usul blan taqsmot unsyasn muls bo ycha jut va toq unsyalarga yoyb,un ltron nrgyas bo ycha o rtachalasa, ( ( ( ( δ δ 3 3 Enrgya bo ycha taqsmot unsyasga ga bo lamz.bun tborga olb, (..n (.. ga qo yb, un omy nrgya srt bo ycha o rtachalanganan yn ( unsya uchun quyag tnglamaga ga bo lamz [7]: ( ( ( ( ( ( [ ] [ ] I I E Д E E Д Д t, (.. Bu yra
Д ( To zchlg sa brlgan hola j ( m 3 ( v I 3 δ ( 3 δ v Д 3 π shala tola. ( ( ( E Д ( ( (..3 Bz bu yra tovush to lqn mayon tomonan ltronlarnng qzuv stat mayon tomonan bo lagan qzshan o ra muhmroq bo lgan holn o rayotganmz uchun, lgusa omy ltr mayon tomonan bo lagan qzshn tborga olmaymz. (,, t unsyan sn o zgaruvch qsm ( an va tz o zgaruvch qsm (,, t an borat b qaraymz: (,, t ( (, t (..4, (bu yra (, yan ( ustga qo ylgan chzq tovush to lqn avr bo ycha olngan o rtachalash b tushunla. Bznng ta rmzga o ra (,, t bo la. (.. n tovush avr bo ycha o rtachalaymz: Д I ( Д ( [ ] I [, ] I [ ] (..5 Bu tnglaman (.. tnglamaan ayrshan hosl bo lgan tnglama (, t taz o zgaruvchan taqsmot unsyas uchun yozlgan tnglama, hsoblana:
( ( ( ( ( ( ( [ ] [ ] [ ] I I I Д Д Д Д Д Д t,, (..6 Bz, 3 ω ω ( ω hol [6] sha qaralgan bo lgan hollarn qaraymz. Bu shartlarga [3] srmnt mos la. (..6 tnglamanng cha tomona joylashgan halarn baholaymz. Ular tartb jhatan quyagcha attallar hsoblana: Д Д Д Д t :: ; ω ( ( Ä Ä Ä ; Bz Д ω b hsoblab, (..6 nng barcha halarn Д ga bo lb chqsa, o ramz uchun nt tnglama uchl soalasha (bza,, ω ϕ va quyag ychmga ga bo lamz: ω ϕ Д Д (..7 uhm br holn shu yra o rsatb o tamz. Konsntratson nochzqlnng chlg, yan ϕ bo lganlg, shunga olb la, qzuv nochzqla qaramasan tovush to lqnng shal o zgarmay, u qanay snusoal bo lgan bo lsa,shunay snusoal bo lb qolabra. Lb ayn shu ayta taqsmot unsyas uchl o zgara. (..7ag ( unsya (.. tnglamanng tovush avr boycha olngan o rtachasan tola ( [ ] [ ] I I Д, (..8 Bu yrag o zgaruvchlarn ury tasavvura ( [ ] [ ].. q t ω,
ab tasvrlab, ω [ [ ( t ]..] q Д ( j j R ω Д * ( n olamz. Agar Д * ( Д ( [ Д ( ] j ; Д ( ( Д ; tngllar o rnl b olnsa, ( unsya uchun [ Д ( ] Д ( ω Д ( Iˆ, ω [ ] [ ] Iˆ [ ] q, tnglamaga ga bo lamz. Bu yra shlatlgan Д q ( orqal Д, ( qq (..9 blglangan. Bu yra qay qlb o tamz, tovush to lqn bo lmagana va ltronlar aro to qnashuv hsobga olnmagana (..8 tnglama [8] maqolaa ltrlgan [] tnglamaga o shash bo la. Shubay qlb, tovush to lqn mayona taqsmot unsya ( uchun tnglamaga ga bo l. Bu tnglamaan o rna, (..8 a shtro tagan otsyntlar uzya tnzor Д, ( nng omonntalar blan anqlana. Shunng uchun bz Д, ( tnzorn tyory magnt mayon H a hsoblaymz. Bunay hsobn o tazsh uchun tsar orator I nng v vtorga ta sr anqlashmz zarur bo la. I oratornng mulsnng tyory unsyas ϕ ( ga ta srn quyag tnglamalar blan anqlaymz. Y ( I ϕ( ϕ( ΞY ( yo Y I Y ( ( ( v H c ϕ ( (.. (..
Bu yra muhm br hol qay qlsh lozm [3]. orator, chun I Y ( ϕ ( tnglaman const I br qymatl bo lmagan Y ( ( n -ltronlar onsntratsyas ychm qanoatlantra. n Shunng uchun qo shmcha shart I ϕ( bajarla b olamz. Bunan tashqar bz o rayotgan unsya uchun I Y ( (.. (..3 shart bajarlgan bo la. Bza qaralayotgan Ξ ˆ orator ϕ ( (..4 Shartn qanoatlantruvch unsyalar lassa anqlngan bo la. Bznng hola ϕ ( v bo lgan uchun (.. o rna tnglaman yoza olamz. Y I Y ( ( ( v H c v (..5 agnt mayon H yo nalsh OZ - o q bo ylab yo nalsn. U hola, y tslgan Onzagr o zgaruvchlar ( v, ϕ Y ( ( I Y Ω v ga o tb, (..5 o rna (..6 tnglaman olamz. Bu yra n Y ( v, ϕ, η laran bog lq bo lgan vtor, η Y vtor va magnt mayon orasag burcha, omonntalar Y Y snη cosϕ Yy Y snη snϕ Y Y cosη z H Ω - slotron chastota. Y vtor mc (..7 Bu yra Y aqat nrgyaga bog lq bo lgan unsyar. (..7 sr garmonalar to qnashuv oratornng ususy unsyalar bo lgan uchun I Y Y (..8
b yozshmz mumn bo la. (..8n hsobga olgan hola (..7 tnglama o rna tnglamalar sstmasga ga bo lamz: Ω Ω η ϕ ϕ ϕ ϕ cos sn cos v Y v Y v Y z y (..9 bu yra η sn,, y z Y Y. En y Y Y Y blg rtb va ϕ Y b hsoblab, (..9 an (..6 nng ychmn osonl blan toamz. Y unsyanng omonntalar o rnsh quyagcha bo la: ( ( Ω Ω Ω Ω z z y y y v Y v v Y v v Y ; ; (.. v I Y n (..7ga qoyb, uzya tnzor omonntalarn toamz: ( ( ( ( ( ( ( ( ( ( ( ( Ω Ω Ω ; ; y y z y z z z y y v Д Д Д Д v Д v Д Д (.. Agar magnt mayon chl bo lsa, yan Ω bo lsa, (.. o rna quyaglarga ga bo lamz ( ( ( ( ( ( Ω Ω ; v Д v Д v Д Д y z z y y (..
Tovushnng tarqalsh oa tuvch tnglamaga Д ( tnzor omonntalarnng ombnatsyas qatnasha. Д ( uchun (..6an oyalanb, toamz: Д ( sn θ Ω cosθ (..3 v ( Ω [ ( ] bu yra θ -tovush to lqn vtor va magnt mayon o rtasag burcha Ω hola Д v ( sn θ Ω cos θ (..4 ( Ω [ ( ] En bz azovy srsya roln baholovch (..5 tngla qaytamz. Unga (..4n qo yb, tngszln olamz. Bu yra ( R sn θ ( Ω cosθ q [ ] R v Ω (..5 -ltron orbtasnng Larmor bo ycha raus. (..5 shart quyag ma noga gar. Agar tovush magnt mayon yo nalsha tarqalayotgan bo lsa ( cos θ azovy srsya muhm mas. Bunng uchun tovush to lqn uzunlg v an ancha atta bo lmog ra (yan. π ltron rn chosh yo l uzunlg Tovush o nalang tarqalayotgana rn chosh yo l uzunlg roln ltron orbtasnng aratrl o lcham-larmorcha raus R o ynay. (..5 shart Ω bo lgana θ burchaa jua bog lq bo la. Bu holatn nazary hsoblarn srmnt natjalar blan solshtrgan vaqta jua muhmr va un hsoban chqarmasl lozm bo la. (..8 tnglamanng cha tomon attal tartb bo ycha ( aramtr blan anqlana. Bu ramtrnng onsntratson nochzql aramtr nsbat [ ] ( ( sn θ ( Ω cosθ Д Д R (..6
tngl blan anqlana. Bunan o rna, sochlsh vazlast sochlsh ( bo lgana (..6 attal hatto [ ] ( R sn θ ( Ω cosθ bo lgana ham jua atta bo lsh mumn. Bu hola qzuv nochzqlg onstratson nochzqlan ancha ustun bo la. En bz stat mayon E tomonan chaqrlagan qzuvnng hsobga olmasl monyatn baholaymz. Bunng uchun (..7nng cha tomon 3 Д ( E E (..7 attal blan solshtrb o ramz. (..7ha stat mayona qzsh aramtr hsoblana. Bu aramtrlar nsbat ( Ω θ ( Ω sn θ cos E attalga bo la. nng qymatan (lgus mavzuag (9ormulaga qaralsn! oyalanb, tovush ntnsvlg uchun quyagn olamz: Agar (..8 n n InSb ( Ω ( Ω cosθ E w S (..8 χ sn θ uchun 5 lorstl o nalang magnt mayona va qymat tovush uchaysh ostonasa bo lgan omy ltr mayona 3 baholamoqch bo lsa, u ntnsvl uchun S 6 n bra. (..4 tnglamanng ychm to qnashuv oratornng brlshga bog lq bo la. Bu yra holnng yuzaga lsh mumn:. bo lsn. Bu hol ltronlararo o zaro to qnashuv hal qluvch ahamyatga ga bo la. Bu hola ltronlarnng taqsmot unsyas nrgya bo ycha asvll unsyas bo la va unng tnraturas T ( c Vt sm T T bo la: (..9
Bu yra T ltron sstmanng to lq nrgoyas uchun balans shartan tola: Д ( Iˆ [ Д ( ] [ Д ( ] [, ] ω ω Iˆ [ ] Nolastl bo ycha yo qalb tmaygan ng ch yaqnlashuva I [ ] A( T (..3 (..3. bo lsn. Bu hola ltronlararo o zaro to qnashuv muhm rol o ynamay, un hsobga olmasa ham bo la. Taqsmot unsya bu hola quyag o rnshga ga bo la: Bu yra T ( u c ξ g( ξ ξ (..3 g ( Д T ( Д ( Д ( ω [ ] [ ] ω qzuv unsyas, c otsynt bo lb, normallashtrsh shartan tola. (..33 Eltronlar taqsmot unsyasn hsoblash orqal tovushnng yutlsh (uchayshn hama ultratovush tzlgnng o zgarshn - hollara tosh monn bra...ultratovushnng yutlsh (uchaysh otsynt Olng mavzulara qay qlganmz, ultratovushnng muhta tarqalsh lastl nazaryas tnglamas, Puasson tnglamas, uzluszl tnglamas va to zchlg tnglamas blan tavslanar. Bu aragraa bz tovush to lqn tomonan yuzaga lagan va muhta ltr mayonn qayta taqsmlanshga sababch bo lagan austoltr tn hsobga olmaymz [9]. Bu tn
aloha qarab chqamz. U hola to zchlg uchun tnglaman quyagcha yoza olamz: j ϕ n n µ ( ω, Д ( ω, nv ( (.. ω, Bu yra µ ( ω, q, Д ( ω, q, V ( ω q attallar mos ravsha tv laml,, t uzya otsynt, tv ry tzlg ma nosn bruvch attallar bo lb, ular quyagcha anqlanalar [ 8 9]: Bu yra ( m 3 V µ Д A, n 3 q π A n ( ω, Д ( (.. ( ω, A Д ( (..3 ( ω, E A Д ( (..4. Yuqora qay qlb o tlgan tnglamalar sstmas va to zchlg uchun yozlgan (..-tnglamaan tovushnng srson tnglamasn tosh mumn. Bu hola tovush to lqn vtorga tolagan tuzatma quyag o rnshga ga bo la: χ Д ( ω, ( ω, Д ( ω, ( ω, ω bu yra [ ] V ( ω, [ ] ( ω, - tv rlasatsya vaqt. 4π n µ ( ω, Eltron tmratura T n hsoblash uchun b olamz. Bu yra A ( T 3 T u, ( T γ (..5 u, γ lar son bo lb, nrgya va mulsnng sochlsh manzmn o rsata. asalan, ormatsya- aust sochlsh uchun, γ u ; yzoaust sochlsh uchun aralashmalara sochlsh uchun γ 3., γ u ; onlashgan
Eltron tmratura quyag balans tnglamaan tola: ( ( g u T Г T T T T T u (..6 Bu yra ( Г - Eylrnng gamma-unsyas. (..6 tnglamanng ychmn tosh ancha muraab bo lganan unng ychmn uchl qzsh ( T T mavju bo lgana toamz. Ychmn H, H va H bo lgan 3 - hola (bu yra Ω b hsoblaymz ltramz. T T n hsoblash natjalarn quyag javala ltrlmoqa: ( ω Д hola qavs cha turgan oa oy ga o aytrla. Eltron tmraturas uchun hsoblangan natjalaran oyalanb, tv laml, tv uzya otsynt va tv ry tzllarn toshmz mumn. Natjaa tovushnng yutlsh (uchaysh otsynt va tovush tzlgnng o zgarsh uchun ormulalarn tovushnng ntnsvlgan bog lq ravsha toa olamz: ( ( [ ] 3 V V G ω η ω χ (..7 ( [ ] ( [ ] 3 3 3 V V w w ω η ω η η χ (..8 H, H H ( Ω ω D ( ( 6 γ γ u u Г Г mt ( ( ( 6 Ω γ γ u u Г Г mt
Agar (..7-..8 natjalarn.nng (..-.. ormulalar blan solshtrsa, o ramz ltronlarnng qzsh V V, η η o zgarshlarga olb ra an.,, 3 unsyalar szlarl arajaa sochlsh manzmga bog lq bo lgan unsyalar hsoblana va ular yutlsh (uchaysh otsynt hama tovush tzlg qymatnng o zgarshga olb la. Bu unsyalar javallara ltrlmoqa. Kuchl qzsha va ltron tmraturas bo lmagan hola ormula orqal brluvch ( unsya arajasa turgan oanng mahrajag (br n tashlab (hsobga olmasl tsh mumn. U hola unsya arajasag ntgraln ntgrallab bo la va hsob T mavju bo lgan hol bajarla. Hsob natjalar -javala ltrlgan. Shun qay qlmoq ra, o tazlgan hsob natjalar u ± γ shart qanoatlanganagna to g r bo la, as hola unsya arajasag ntgrala masusl ayo bo la. Qzsh aramtr oasga ruvch tovush to lqn yaratgan ltr mayon 3 uchlanganlg varat nng tovush ntnsvlg blan bog lansh - nng (.-..4 va (..8 ormulalaran tola va unng o rnsh quyagcha bo la: 3 4π η χ w η 3 4 [( ω V ] [( ω V ] Shunay qlb, tovush yutlsh otsynt, unng tzlg o zgarshnng ntnsvla bog lqlgn turl chastotalar sohasa, tmraturaa va ry mayon qymatlara taqq qlsh yo l blan o tazgchlara ltronlar sochlsh manzmlarn anqlash mumn bo la. [33] maqolaa qay
qlnshcha, o tazlgan baholashlar va srmnt bz qarab chqqan tlarn tajrbaa to g ran-to g r uzatsh mumnlgn o rsata. II bob bo ycha ulosa Bu boba ham uzun to lqn uzunla ga bo lgan tovushnng yzoltr ossaga ga bo lgan yarmo tazgchlara tarqalsh qarab chqlganr.agar - boba qaralgan yarmo tazgchlara ltron nrgyasnng rlasatsya vaqt ancha ch qymatga ( s ga bo lb,u uchun << (bu yra - ltronlarnng o zaro to qnashuv orasag vaqt yo ltron mulsnng rlasatsya vaqt shart bajarla.ii boba o rlgan hola qaralgan yarmo tazgchlar ltronlar ch tv massaga va yuqor lamla ga bo lganllar bos tovush bu yarmo tazgcha yuzaga ltrgan ltr mayona bu ltronlarnng qzsh yuzaga la va natjaa ancha atta szlarl 7 qymatga ga bo la ( s >>.Bunay sharota ω >> tngszlg bajarla hama ltronlar qzuv sor bo la.bu sa qaralayotgan sstmanng muvozanat holatan nomuvozanat holga olb o ta.brlgan holata -bobag tovushnng tarqalshn lass tnglamalar orqal oalab bo lmay va brlgan masala uchun Boltsmannng nt tnglamasn ychshga to g r la.bu usul blan tolgan tovushnng yutlsh va uchaysh ormulas -boba qaralgan Uaytnng ormulalaran muhm arq qlshga olb lsh mumn an.bunay usula qurlgan nazarya n chzql nazarya bo lmasan,nochzql nazarya hsoblana.bunay nazarya astlab mosval olmlar Gulyayvlar tomonan va Parayv O.P. tomonan brlgan.
III BOB. YARIO TKAZGICHLARDA ULTRATOVUSHNING YUTILISHI VA KUCHAYISHI HAQIDA 3.. Domy ltr mayon bo lmagana ultratovushnng yutlsh Qaralayotgan hola ultratovushnng yzoltr yarm o tazgchlara tarqalshn tavslovch lass tnglamalarn yozb bo lmay va [ 33 34] lara qlngan Boltsmannng nt tnglamasn ychshga to g r la.una shtro tuvch taqsmot unsyasnng vaqt bo ycha tz o zgaruvchan qsm omy ltr mayon mavju bo lmagana quyagcha o rnshga ga bo la: D ( ϕ ω D ( (3.. Bu yra D ( D (, D ( uzya tnzor, tovush to lqn avr, bo ycha o rtachalangan taqsmot unsyas. o rtachalangan nt tnglamaan tola Bu unsya vaqt bo ycha E ω D ( Iˆ [ ] I [, ] (3.. ω [ D ] ( (3..a I [ ], I [, ] mos ravsha to qnashuv ntgralnng nolast qsm va ltronlararo to qnashuv ntgral, E tovush to lqn yzoltr mayonnng amltuas. Tovushnng yutlsh otsyntn hsoblash uchun (3..n tnglaman ychsh va bu ychmn (3..ga qo ysh talab tla.bz ltronlararo to qnashuvn muhm,ya n <<, b hsoblaymz hama unsyan T - ltron tmratural masvllcha unsya b olamz.krtlgan ltron tmraturan nrgyanng balans tnglamas bo lgan