ECE507 - Plasma Physics and Applications

Transcription

1 ECE57 - Plasa Physcs and Applcatons Lctur Prof. Jorg Rocca and Dr. Frnando Toasl Dpartnt of Elctrcal and Coputr Engnrng

2 Introducton: What s a plasa? A quas-nutral collcton of chargd (and nutral) partcls whch hbts collct bhaor. ECE 57 - Lctur

3 Eapls of naturally occurrng plasas: (99% of th sbl unrs s a plasa) Gas bula Lghtnng Flas Aurora Borals Solar Corona ECE 57 - Lctur

4 Eapls of an-ad plasas: Fluorscnt laps (glow dscharg) Flat panl plasa dsplay Plasa torch Plasa tchng ractor (plasas play portant rol n th anufacturng of ntgratd crcuts) Z-pnch Lasr-cratd plasas ECE 57 - Lctur 4

5 Partcls found n plasa utral and ond atos Dnsts: () = on charg Fr Elctrons Photons ρ( ) f ( = ) th plasa s partally ond f ( = ) = th plasa s copltly ond (no nutral atos) All ths partcls ntract wth ach othr and wth lctrc and agntc flds akng th plasa a ry copl syst Elctrons Ions () ρ() Photons ECE 57 - Lctur 5

6 Plasa Paratrs Plasa Dnsty Elctron tpratur Ion tpratur Man on charg T T Z () : on charg Ths plasa paratrs dtrn portant plasa proprts Eapls Dby scrnng dstanc (dstanc byond whch nddual chargs tnd to b scrnd by othr narby chargs) λ D ε Elctrcal rsstty: η π 4π ε ln Λ ( ) Whr lnλ s th Coulob logarth Plasa frquncy (natural frquncy at whch lctrons tnd to oscllat) ω p ε ECE 57 - Lctur 6

7 Th Concpt of Tpratur A gas has partcls of all locts If a suffcntly larg nubr of collsons occurrd btwn ths partcls th ost probabl dstrbuton of ths locts s known as th Mawll Dstrbuton For splcty lts consdr a gas n whch th partcls can o n only on drcton (.g. chargd partcls n a strong agntc fld). Th on dnsonal Mawll Dstrbuton s gn by: f( ) (.) f( )d s nubr of partcls pr wth locty btwn and +d ½ s th kntc nrgy p( k =.8 - J/K s Boltann s constant A /) Th dnsty of partcls pr s f( ) d (.) A s a noralaton constant rlatd to dnsty A (.) π - ECE 57 - Lctur 7

8 Th Concpt of Tpratur Th wdth of th dstrbuton s charactrd by a paratr T w call th Tpratur f( ) T > T T s rlatd to th arag kntc nrgy E AV W wll dfn th thral (ost probabl) locty as E a - ( T - f( T ) f( ) d Th ) d (.4) (.5) Gaussan functons, σ = Substtutng (.5) n (.) f( Th ) p A Th (.6) (.7) ECE 57 - Lctur 8

9 Th Concpt of Tpratur Dfnng Υ (.8) Th f() A p(-y) (.9) Substtutng n.4 (and ultplyng and ddng by Th to for Y) E A A Th - p -Y Y dy (.) Intgratng th nurator by parts: - Y p -Y YdY p( Y )Y p -Y p( Y ) dy dy (.) ECE 57 - Lctur 9

10 Th Concpt of Tpratur Suarng E A Th a / (.) E a Arag kntc nrgy n on dnson (.) ECE 57 - Lctur

11 Th Concpt of Tpratur Mawll s locty dstrbuton n thr dnson can b wrttn as f(, y, ) A p y / (.4) Th arag kntc nrgy s E a A A A Th prsson s sytrc n, y, snc th Mawll dstrbuton s sotropc E a A A p π y p y p y / d / p / d p y / d p / y y d d / d d d d d y y d d y (.5) (.6) (.7) E a Arag kntc nrgy n thr dnsons (.8) ECE 57 - Lctur

12 Th Concpt of Tpratur Snc T s so closly rlat to E a t s coon n plasa physcs to g th tpratur n unts of nrgy. To aod confuson n th nubr of dnsons nold t s not E a but th nrgy corrspondng to that s usd to dnot tpratur J For V.6 J T -.8 J/ K,6 9 o o K V,6 K By V usually w an: = V E a = V n thr dnsons ECE 57 - Lctur

13 Tpratur s an qulbru concpt otc that to dfn th prous rlatons w assud a Mawllan dstrbuton. If two groups of partcls wth dffrnt locts ar allowd to undrgo a suffcnt nubr of collsons, thy wll ntrchang nrgy and thral acqurng a Mawllan dstrbuton. Mono-nrgtc dstrbuton Collsons F F on-mawllan dstrbuton Mor collsons Mawllan dstrbuton (thralaton has occurrd) F F M Th Mawllan dstrbuton s dfnd by only on paratr: th tpratur T f( ) A p ECE 57 - Lctur

14 Elctron, Ion and Atoc tpraturs Elctron, on and atos n th sa plasa can all ha dffrnt tpraturs Th ntrchang of nrgy n collsons btwn partcls of qual ass s larg (apls: collsons btwn lctrons and lctrons, ons and ons) Th - collson rat >> - collson rat Thrfor lctrons tnd to b n thral qulbru wth othr lctrons and ons wth othr ons, but oftn thy ar not n qulbru wth ach othr. F T = lctron tpratur Ths stuaton rqurs a dffrnt tpratur to dfn ach group f ( ) A p( / ) F T = on tpratur f ( ) A p( wth T T / ) ECE 57 - Lctur 4

15 Thralaton Elctrons and Ions ar oftn n Thral Equlbru wth thsls but not wth ach othr Eapls: Glow dschargs (on sgn, H- lasr dscharg) T > T Thta Pnch (Magntcally coprssd plasa T > T T Th lctron-lctron qulbraton t s uch - collsons shortr than th lctron-on qulbraton t Equlbraton ts n sconds (L. Sptr Physcs fully ond gass) τ q Elctron-lctron qulbraton t ( ) - collsons Eapls: A carbon lasr-cratd plasa: T = 5 V, =, Z = q q 66. ( - ) ( - ) 4 T s.98 8 [T ] = V, [ ] = c ( ) s fs s ps 98. At t ps T T Ths otats two tpratur plasa odls τ Elctron-on qulbraton t 8 q ECE 57 - Lctur 5 Z T s T = Z an

16 Mawll spd dstrbuton Th fgur blow shows th gotrcal ntrprtaton of th spd dstrbuton functon, and also srs to llustrat th conrson fro locty coordnats (, y, ) to that of spd,. E y - f d f,y, ddyd 4π d Thr-dnsonal locty spac f() f π Mawll spd dstrbuton p 4π ECE 57 - Lctur 6

17 ECE 57 - Lctur 7 Mawll spd dstrbuton Th roth ont of th spd dstrbuton functon (qual to th ara undr th functon) s qual to th partcl dnsty: Th frst ont of th locty dstrbuton s th arthtc an spd, an thral locty, or arag agntud of th locty: d f = / u u u π π f d p 4 d 4 p d / / / 8

18 Mawll spd dstrbuton Th scond ont of th spd dstrbuton functon s rlatd to th root an squar spd of th partcls (rlatd to th arag nrgy): rs f d π π / / rs 4 4 Th ost probabl spd (so ts calld thral locty) s calculatd by dffrntatng th dstrbuton functon onc and sttng t qual to ro: p 5/ u 4 d p u 8 du d d p th / ECE 57 - Lctur 8

19 Mawll spd dstrbuton Th spd dstrbuton can b rwrttn as a functon of nrgy usng th rlaton btwn spd and nrgy: E f(e) π E p E Mawll nrgy dstrbuton Prforng slar calculatons to thos n prous slds, you can asly show that th ost probabl nrgy and th an nrgy ar gn by E E ECE 57 - Lctur 9