SIMILARITIES BETWEEN INTENSE e AND ν BEAMS IN PLASMA. Robert Bingham

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1 SIMIARITIES BETWEEN INTENSE AND BEAMS IN PASMA Robrt Bingham Ruthrford Applton aboratory,chilton, Didcot, Oxon. OX11 0QX Collaborators.O.SIVA, J.T.MENDONCA, W.MORI, P.K.SHUKA ORION WORKSHOP, SAC, EBRUARY 003

2 ABSTRACT Thr is considrabl intrst in th propagation dynamics of nutrinos in a bacground disprsi mdium, particularly in th sarch for a mchanism to xplain th dynamics of typ II suprnoæ and sol th solar nutrino problm. Nutrino intractions with mattr ar usually considrd as non slf-consistnt singl particl procsss. W dscrib nutrino straming instabilitis within suprnoæ plasmas, rsulting in longitudinal and transrs was using coupld intic quations for both nutrinos and plasma particls including magntic fild ffcts. Ths instabilitis ar quialnt to th -bam plasma instabilitis but ar dscribd by th lctrowa coupling rathr than th lctromagntic coupling. Employing th rlatiistic intic quations for th nutrinos intracting with lctrons in a plasma ia th wa intraction forc w xplor th diffrnt collcti plasma instabilitis drin by nutrinos. W xamin th anomalous nrgy transfr btwn th nutrinos and th bacground plasma ia xcitation of lctron plasma was (nutrino straming instability), and th gnration of quasi-static B filds (lctrowa Wibl instability). Th rlatiistic intic quations in th prsnc of strong xtrnal magntic filds will b drid and th influnc of th axial ctor potntial for nutrinos propagating in a magntizd plasma on ths instabilitis will b prsntd. Th prsnc of th magntic fild gis ris to a nw rout for flaour oscillations as wll a nw forc trm that may b rsponsibl for pulsar ics. Th rlanc of th lctrowa plasma instabilitis for th xtrm conditions occurring in th lpton ra of th arly unirs, suprnoa, and gamma ray burstrs is pointd out. inally, a comparison will b mad with th physics of intns photon and lctron bam drin plasma was.

3 Outlin Intns fluxs of nutrinos in Astrophysics Nutrino dynamics in dns plasmas (maing th bridg with HEP) Plasma Instabilitis drin by nutrinos Suprnoa, nutron stars and drin plasma instabilitis Gamma-ray burstrs: opn qustions + - 3D lctromagntic bam plasma instability Consquncs on GRBs and rlatiistic shocs Conclusions and futur dirctions

4 Motiation Nutrinos ar th most nigmatic particls in th Unirs Associatd with som of th long standing problms in astrophysics Solar nutrino dficit Gamma ray burstrs (GRBs) ormation of structur in th Unirs Suprnoa II (SN II) Intnsitis in xcss of W/cm and luminositis up to 10 5 rg/s

5 Nutrinos in th Standard Modl ptons Elctron Muon µ Elctron nutrino Muon nutrino µ Tau τ Tau nutrino τ An lctron bam propagating through a plasma gnrats plasma was, which prturb and ntually bra up th lctron bam Elctrowa thory unifis lctromagntic forc and wa forc A similar scnario should also b obsrd for intns nutrino bursts

6 ngth scals Compton Scal HEP Plasma scal λ D, λ p, r >> 14 ordrs of magnitud Can intns nutrino winds dri collcti and intic mchanisms at th plasma scal? Bingham, Bth, Dawson, Su (1994) Hydro Scal Shocs

7 Non-inar Scattring Instabilitis Rapidly falling matrial Rgion coold by nutrino andau damping Stalld shoc front Hot nutrinos Proto-nutron Star Rgion hatd by nutrino-plasma coupling

8 Non-inar Scattring Instabilitis Sourc GRB is Producd hr? optical or UV, dcays quicly bgins as?-rays or X-rays & continus as th lat aftrglow nutrinos ISM intrnal shocs forward xtrnal shoc shoc rrs shoc

9 Suprnoa IIa physical paramtrs To form a nutron star rg must b rlasd (graitational binding nrgy of th original star) light+intic nrgy ~ rg graitational radiation < 1% nutrinos 99 % Elctron m: n 0 ~ cm -3 Elctron m: T ~ MV Dgnracy paramtr Θ = T /E ~ Coulomb coupling constant Γ ~ nutrinosphr~ rg/s Km ~ W/cm Duration of intns burst ~ 5 ms (rsulting from p+ n+ ) Duration of mission of all flaors ~ 1-10 s

10 Suprnoa Explosion How to turn an implosion into an xplosion Nw nutrino physics? mfp for? collisions ~ cm in collapsd star? mfp for collcti plasma-nutrino coupling ~ 100m How? Nw non-linar forc nutrino pondromoti forc or intns nutrino flux collcti ffcts important Absorbs 1% of nutrino nrgy sufficint to xplod star Nutrinosphr (proto-nutron star) Nutrino-plasma coupling Plasma prssur Shoc Phys. tt. A, 0, 107 (1996) Phys. R. tt., 88, 703 (1999)

11 Nutrino dynamics in dns plasma Singl particl dynamics gornd by Hamiltonian (Bth, 87): H = p c + m c 4 + G n (r, t) G - rmi constant n - lctron dnsity pond = G n (r,t ) orc on a singl lctron du to nutrino distribution Pondromoti forc * du to nutrinos pushs lctrons to rgions of lowr nutrino dnsity * pondromoti forc drid from smi-classical (.O.Sila t al, 98) or quantum formalism (Smioz, 87) Effcti potntial du to wa intraction with bacground lctrons Rpulsi potntial = G n (r,t) orc on a singl nutrino du to lctron dnsity modulations Nutrinos bunch in rgions of lowr lctron dnsity

12 Nutrino Rfracti Indx Th intraction can b asily rprsntd by nutrino rfracti indx. 4 Th disprsion rlation: ( E V ) p c m c = 0 (Bth, 1986) E is th nutrino nrgy, p th momntum, m? th nutrino mass. Th potntial nrgy V = G n G is th rmi coupling constant, n th lctron dnsity Rfracti indx c cp N = = ω E N 1 h G c n Not: cut-off dnsity ε nutrino nrgy n c > ε G Elctron nutrinos ar rfractd away from rgions of dns plasma - similar to photons. n? n

13 Nutrino Pondromoti orc or intns nutrino bams, w can introduc th concpt of th Pondromoti forc to dscrib th coupling to th plasma. This can thn b obtaind from th nd ordr trm in th rfracti indx. N 1 Dfinition POND = ξ [andau & ifshitz,, 1960] whr? is th nrgy dnsity of th nutrino bam. b N = 1 G n n? is th nutrino numbr dnsity. ε Pond Pond G n = n G n ξ ε

14 Nutrino Pondromoti orc () orc on on lctron du to lctron nutrino collisions f coll Total collisional forc on all lctrons is mod σ mod is th modulation wanumbr. or a 0.5 MV plasma s? collisional man fr path of cm. = GBT πh c f = σ ξ s? is th nutrino-lctron coll coll = n f = Pond coll = coll 3 π h c G T B 3 n σ ξ Mod Pond coll cross-sction

15 = ω χ ω ω ω χ p p p f d c m n n G ˆ 1 ), ( Kintic quation for nutrinos (dscribing nutrino numbr dnsity consration / collisionlss nutrinos) Elctron dnsity oscillations drin by nutrino pond. forc (collisionlss plasma) 0 1 = + + p J J r f c t c n G f t f Disprsion rlation for lctrostatic plasma was 0 ), ( ), ( 1 = + + ω χ ω χ Elctron suscptibility Nutrino suscptibility Kintic Equation for nutrinos Kintic Equation for nutrinos ( ) 0 1 = f f c t c n G f t f p B E p J J r

16 Gomtry of nutrino mission Nutrino distribution in th nutrinosphr f 0 ( ) r R θ d(r,θ) A θ max r/(r+r) Nutrinosphr Nutrino distribution in A f (,R,θ)= f 0 ( )/d (R,θ) R>>r and θ max 30 mrad for R>>r f(θ)= const. θ < θ max f(θ)= 0 θ > θ max ℵ γ max 1 cosθ max 1 / Bamd distribution Analysis in slab gomtry gis good pictur G and 1/(1-cos θ max ) 10 3

17 Nutrino Bam-Plasma Instability ω =ω p0 Mononrgtic nutrino bam f ( ) 0 = n 0δ p p 0 Disprsion Rlation + m c 4 cos θ ℵ 4 +sin θ c 4 E 0 ω ccosθ p c 0 E 0 If m 0 dirct forward scattring is absnt Similar analysis of two-stram instability: maximum growth rat for 0 = c cos θ ω p0 ω = ω p0 + δ = 0 + δ Wa Bam (δ/ ω p0 <<1) Growth rat Strong Bam (δ/ ω p0 >>1) γ max G 1/ γ max = 3 ω tan θ p0 sin θ ℵ Singl -lctron scattring G θ ^p 0 ℵ= G n 0 n 0 m c E 0 Collcti plasma procss much strongr than singl particl procsss 1/ 3 G / 3

18 Nutrino Bams - d Brogli walngth Nutrino bam with arbitrary momntum distribution f = n χ (ω, ) rom mononrgtic bam to arbitrary nutrino nrgy distribution 1 = λ 0 E 0 πhc < λ > πhc fˆ( p ) δ ( p ) δ ( p 0 0 x y z Nutrino suscptibility n 0 dp (ω cosθ) x 1 ) ˆ f 0 p x 4 43 =<λ > / πh <λ > is th arag d Brogli walngth of nutrino distribution or distributions with qual nutrino dnsity n 0 and qual d Brogli walngth <λ >, growth rats ar idntical

19 Rol of lctron-ion collisions in th instability (hydro) BGK modl of collisions Nw disprsion rlation χ ( ω, ) = ω ω ( ω p + i ω (ω + i i )= ω p0 + m c 4 cos θ + sin ℵ 4 θ c 4 E 0 ω ccosθ p 0c E 0 Similar analysis as bfor lads to s ) s i Elctron-ion collision frquncy γ max = ω tan θ p0 sin θ ℵω p 0 i (with collisions) 1/ G / 3 s γ max G (without collisions) Instability thrshold is G sinc it is proportional to (Damping lctrons) x (Damping nutrinos)

20 Instability rgims: hydrodynamic s intic N σ φ, If rgion of unstabl PW mods orlaps nutrino distribution function intic rgim bcoms important 0 Unstabl PW mods (ω, ) N 0 = 10 9 cm -3 = 10 5 rg/s R m = 300 Km <E > =10 MV T = 3 MV m = 0.1 V Kintic instability γ G if ω 0 << σ σ /c Hydro instability γ G /3 if ω 0 >> σ ω c 0 c γ max ω p0 β φ whr = p c /E = p c /(p c +m c 4 ) 1/ - for m 0, σ 0 hydro rgim -

21 Estimats of th instability growth rats n 0 =10 9 cm -3 = 10 5 rg/s R m = 300 Km <E >=10 MV Growth distanc ~ 1 m (without collisions) T < 0.5 MV T < 0.5 MV T < 0.1 MV Growth distanc ~ 300 m (with collisions) - 6 m for 0 -foldings - T =0.5 MV Man fr path for nutrino lctron singl scattring ~ m