c = ω k = 1 v = ω k = 1 ²µ

Transcription

1 3. Electromagtic Wave 3.5. Plama wave A plama i an ionized ga coniting of charged particle (e.g., electron and ion). Variou wave can be excited eaily in a plama. Wave phenomena have been an important ubject in the plama reearch community. The plama i arly charge utral. So the ~E = 0 till hold. However, ither the conduction current nor the diplacement current can be ignored. Wave in plama i different from the wave in vacuum and in conductor Effective Permittivity in a Plama In vacuum, the phae velocity of an EM wave i: c = k = 1 ²0 µ 0 Thi can be geralized for phae velocity of wave in matter: v = k = 1 ²µ In plama µ = µ 0,but² 6= ² 0. Electric field, magtic field, and gerally any quantity in plama can be divided into two part: DC part that doe not depend on time and part that aociated with wave: Q total = Q DC + Q(~r, t) We tudy now only the part aociated with wave, Q, andaume Q = Q 0 e i(~ k ~r t) In plama, the current i predominately carried by electron, a in a conductor, becaue the ma of a electron i mall compared with that of ion. The electron in plama experience the electric force and uffer from colliion with ion. The velocity of electron ha been derived before (when we tudy wave in conductor): e ~v = E m(ν i) ~ ~j = E m(ν i) ~ if there i no DC magtic field (So we can ignore ~v B ~ term in the equation of motion). 1 /note1

2 In mot cae, the electron denity, and thu the colliion frequency ν, are much maller than in conductor. So: ~j ' E mi ~ = i E m ~ The 4th Maxwell equation become: B ~ = µ 0 i E m ~ + ² ~ E 0 t Ã! = µ 0 i E m ~ i² 0 E ~ Ã! = i² 0 µ 0 1 ~E m² 0 Let p = Plama frequency m² 0 and recall H ~ = B/µ ~ 0,wefind H ~ = i² 0 1 p ~E For low frequency wave, p À, conduction current dominate (like wave in a conductor). For high frequency wave, p, diplacement current dominate (like wave in vacuum). If we defi an effective permittivity in plama, ²() =² 0 1 p, The 4th Maxwell equation for a monochromatic pla wave in plama become H ~ = i² E ~ = ² E ~ t, imilar to the equation for a monochromatic pla wave in the vacuum, except ε 0 ε. Therefore, all the reult for wave in vacuum can be ued in plama wave with the modification ε 0 ε. Note that the effective permittivity in plama depend on the frequency. Notealo²<² Diperion Relation /note1

3 The phae velocity of plama wave: v = k = 1 µ² 1 1 = q µ0 ² 0 1 p c = q >c (1) 1 p In plama, ² depend on and thu the phae velocity depend alo on. Thewavein thi cae i diperive. A quare wave contain the fundamental frequency and it higher harmonic. If the phae velocity depend on frequency, it will pread out while it propagate. The dependence of on k i called diperion relation. We can olve eq. (1) for k = c 1 p 1 p = c k = p +(ck) diperion relation in plama 3/note1

4 The diperion relation of EM wave in vacuum i a traight li (non-diperive) with a lope tan α = c. The diperion relation of EM wave in plama i above the li = ck becaue = q p +(ck) ck, but approache the li = ck when k become large becaue = q p +(ck) ' ck when k À p c. Propagation and Reflection of EM Wave in Plama Aume a pla wave propagating in +z direction. From the diperion relation, we obtain ~E = ~ E 0 e i(kz t) If > p (like in vacuum) k = 1 c q p k i real, ~ E = ~ E 0 e i(kz t), wave propagate without decay. If < p (like in conductor) k = i 1 c q p = i k i imaginary. ~E = ~ E 0 e it e k z Wavedecayinz direction and will be reflected. If p, k ' i p = i 1 c δ δ = c p kindepthinplama Short Wave Communication Ionopheric plama (height: 50 km to 100 km) ha a typical denity of /m 3. f p = p π = 1 =8MHz π m² 0 Short wave radio (f 10 MHz) relie on the multiple reflection between the ionopheric plama layer and the earth to reach a ditant receiver. 4/note1

5 Earth i conductor (σ 10 S/m) a long a the impedance Z = iµ0 σ Z µ0 air = which require or σ ² 0 f σ 10 = = 180 MHz π² 0 π For f = 10 MHz, the earth i good conductor Group Velocity According to Eintein relativity, nothing hould propagate fater than the light peed c. In plama, phae velocity v p = k = c q >c 1 p But the phae velocity doe not correpond to the information (ergy) propagation velocity. The information i propagating at the group velocity v g = d dk For non-diperive wave, e.g., EM wave in vacuum, = ck v p = v g = c. In plama, wave i diperive. The group velocity i v g = d dk = c 1 p <c. ² 0 5/note1