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Radiative Processes from Energetic Particles II: Gyromagnetic Radiation

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Radiative Processes from Energetic Particles II: Gyromagnetic Radiation Hale COLLAGE 2017 Lecture 21 Radiative processes from energetic particles II: Gyromagnetic radiation Bin Chen (New Jersey Institute of Technology) Previous lectures 1) Magnetic reconnection and energy release 2) Particle acceleration and heating 3) Chromospheric evaporation, loop e- magnetic heating and cooling reconnection Following lectures: How to diagnose the e- accelerated particles and the environment? • What? • Where? How? Shibata et al. 1995 • When? Outline • Radiation from energetic particles • Bremsstrahlung à Previous lecture • Gyromagnetic radiation (“magnetobremsstrahlung”) à This lecture • Other radiative processes à Briefly in the next lecture • Coherent radiation, inverse Compton, nuclear processes • Suggested reading: • Synchrotron radiation: Chapter 5 of “Essential Radio Astronomy” by Condon & Ransom 2016 • Gyroresonance radiation: Chapter 5 of Gary & Keller 2004 • Gyrosynchrotron radiation: Dulk & Marsh 1982 • Next two lectures: Diagnosing flare energetic particles using radio and hard X-ray imaging spectroscopy 8/3/10 8/3/10 Radio'Emission' Radio'Emission' .'Thermal' bremsstrahlung'(eAp)' .' Gyrosynchrotron'radia5on'(eAB)' ..'Thermal' 'Plasma'radia5on'( bremsstrahlungwAw'(eAp)' )' .' Gyrosynchrotron'radia5on'(eAB)' .'Plasma'radia5on'( wAw)' Radiation from an accelerated charge LarmorLarmor'formulae:'radia5on'from'an'accelerated'charge'''formulae:'radia5on'from'an'accelerated'charge'' 2 2 2 2 dP q 2 2 2q 2 dP q 2 2 2q 2 Larmor formula: = 3 a sin θ P = 3 a d =4 c 3 a sin θ P3c= 3 a dΩΩ 4ππc 3c Rela5vis5c'Larmor'formulae'' Relativistic LarmorRela5vis5c'formulaLarmor'formulae'': € € € € θ" θ" Cases'relevant'to'radio'and'HXR/gammaAray'emission:'' Cases'relevant'to'radio'and'HXR/gammaAray'emission:''Accelera2on#experienced#in#the#Coulomb#field:'bremsstrahlung' Radio and HXR/gammyAccelera2on#experience#in#a#magne2c#field:#-ray emission in flares: gyromagne5c'radia5on' • Acceleration experienced in the Coulomb field: Accelera2on#experienced#in#the#Coulomb#fieldbremsstrahlung:'bremsstrahlung' • Acceleration experienced in a magnetic field: Accelera2on#experience#in#a#magne2c#field:#gyromagnetic radiationgyromagne5c'radia5on' 10 10 Gyromagnetic radiation • Gyromagnetic radiation (sometimes called “gyroemission”) is due to the acceleration experienced by an electron as it gyrates in a B field due to the Lorentz force. • Acceleration is perpendicular to �" 8/3/10 Radio'Emission' .'Thermal' bremsstrahlung'(eAp)' .' Gyrosynchrotron'radia5on'(eAB)' .'Plasma'radia5on'( wAw)' Gyroemission from a single electron Larmor'formulae:'radia5on'from'an'accelerated'charge'' • Let’s start from Larmor’s formula: dP q2 2q2 = a 2 sin2 θ P = a 2 dΩ 4πc 3 3c 3 • Perpendicular acceleration: �$ = �'"�$, where �'" is the (angular) electron Rela5vis5c'Larmor'formulae''gyrofrequency € € "+ �'" = 2��'" = ≈ 2� / 2.8� MHz ,-' θ" • (Direction integrated) Larmor’s equation becomes: 2�5 � = �5 �5 3�8 '" $ • Relativistic case:Cases'relevant'to'radio'and'HXR/gammaAray'emission:'' 9 5" < 5 5 "+ >?- Accelera2on#experienced#in#the#Coulomb#field� = : � �+�$, with �+ =:'bremsstrahlung= ' Accelera2on#experience#in#a#magne2c#field:#8' gyromagne5c=,-' 'radia5on'= 10 8/3/10 Radio'Emission' .'Thermal' bremsstrahlung'(eAp)' .' Gyrosynchrotron'radia5on'(eAB)' .'Plasma'radia5on'( wAw)' Radiation pattern: non-relativistic Larmor'formulae:'radia5on'from'an'accelerated'charge'' • Larmor’s Equation dP q2 2q2 = a 2 sin2 θ P = a 2 dΩ 4πc 3 3c 3 Rela5vis5c'Larmor'formulae'' € € Null at � = 0 θ" � Dipole pattern Observer Cases'relevant'to'radio'and'HXR/gammaAray'emission:'' Accelera2on#experienced#in#the#Coulomb#field:'bremsstrahlung' Accelera2on#experience#in#a#magne2c#field:#gyromagne5c'radia5on' 10 Radiation pattern: relativistic • Relativistic case (� ≫ 1) • In the rest frame of the electron ��E �5 = �5sin5�E �ΩE 4��8 • In the observer’s frame, radiation pattern found from Lorentz transform from the electron rest frame Null occurs at � = ± arccos 1/� Observer Strongly beamed forward along the direction of the electron! Spectrum of Synchrottwn Radiation: A plalitotiiw Discussion 171 from points 1 and 2. The difference 12” - t;’ is less than t,- t, by an amount As/c, which is the time for the radiation to move a distance As. Thus we have AtA = 1: - = 2 (1-4). (6. I Oa) yw, sin (Y It should be noted that the factor (1 - v/c) is the same one that enters the Doppler effect [cf.Relativistic 34.11. Since y>>l. we have gyroemission: sharply pulsed radiation so that 170 Synchrotron Radhtion -I At”~(y~~,sina). (6.10b) Therefore, the width of the observed pulses is smaller than the gyration period by a factor y3. The pulse is shown in Fig. 6.3. From our general discussion of spectra associated with particular pulses, 02.3, we expect that the spectrum will be fairly broad, cutting off at frequencies like l/AtA.If we define a critical frequency a,.E -33 y-w, sina (6.1 la) 2 or vc= -y33 w,sina, (6.1 lb) 47 Figurn 6.2 Emission cones at variouS points of anW accelerated Wparticle's trajectory. f ∆�U ∝ : = 9 = >X = >?- the direction of observation. The distance As along the path can be computed from the radius of curvature of the path, a = As/AB. W ∆� = � end of pulse − � start of pulse From the geometry we∆ �have∝ A0 = 2/y,? so that As = 2a/y.U But the radius of curvature of the path followsU from=> the equation of motion∆� � − ∆� � ∆� � ∆� X = + − = 1 − ≪ = ∆� � � � � � � ym-AV = -vxB,4 At c Figure 6.3 SinceTime-dependence (Av(= v A0 of andthe electricAs = vfiehi At, inwe u havepulse of synchrotron radiation A0 qBsina -=- (6.8a) As ymcv ' V a=- (6.8b) wBsin a ' Note that this differs by a factor sina from the radius of the circle of the projected motion in a plane normal to the field. Thus As is given by 2u As = (6.8~) yw, sin a The times t, and t, at which the particle passes points 1 and 2 are such that As = u(t, - t,)so that 2 t,- t,x yoBsin a ' Let tf and tt be the arrival times of radiation at the point of observation Power spectrum �(�) • For a nonrelativistic electron, radiation field � � is a sinusoid with frequency �'" • Power spectrum is a single tone at the electron gyrofrequency Power spectrum �(�) • As the electron speed picks up, mild beaming effect takes place, � � is non-sinusoidal • Low harmonics of electron gyrofrequency show up in the power spectrum Can you identify two effects in the � � plot? Power spectrum �(�) 184 Synchrotron Radiation 184 Synchrotron Radiation t..(r) + • When the electron is t..(r) + relativistic � � is highly pulsed bJ Figrrre 6lOa Time depmrdence of electric fwiV from a q&'y mooing parti& bJ in a magnetic field (synchrotron radiation). Figrrre 6lOa Time depmrdence of electric fwiV from a q&'y mooing parti& in a magnetic field (synchrotron radiation). • The power spectrum shows contribution from many harmonics Fipw 6 106 Power spectrum for a. Fipw 6 106 Power spectrum for a. 6.7 DISTINCTION BETWEEN RECEIVED AND EMITTED POWER 6.7 DISTINCTION BETWEEN RECEIVED AND EMITTED In about 1968 (e.g., Pacholczyk, 1970; Ginzburg andPOWER Syrovatshi, 1969), it was noticed that a proper distinction between received and emitted power had not been made. (In looking at references beforeIn about then 1968 check (e.g., your Pacholczyk, 1970; Ginzburg and Syrovatshi, 1969), it formulas carefully.) The problem is that the receivedwas pulses noticed are that not aat proper the distinction between received and emitted power frequency wB but at an appropriately Doppler-shifted frequency, because had not been made. (In looking at references before then check your of the progressive motion of the particle toward the observer. This can be formulas carefully.) The problem is that the received pulses are not at the seen clearly in Fig. 6.11. If T= 27r/wB is the orbital period of the projected frequency wB but at an appropriately Doppler-shifted frequency, because motion, then time-delay effects (cf. 94.1), will give a period between the arrival of pulses TA satisfying of the progressive motion of the particle toward the observer. This can be seen clearly in Fig. 6.11. If T= 27r/wB is the orbital period of the projected motion, then time-delay effects (cf. 94.1), will give a period between the arrival of pulses TA satisfying 2a . X-sin'cr. (6.39) *B 2a . X-sin'cr. (6.39) *B Types of gyromagnetic radiation • Gyromagnetic radiation behaves very differently with different electron distributions • A precise general expression valid for all electron energies is not available. Instead, we use approximate expressions for various electron energy regimes v Non-relativistic or thermal (� − 1 ≪ 1): Gyroresonance or cyclotron radiation Thermal v Mildly relativistic (� − 1~1 − 5): Gyrosynchrotron radiation v Ultra-relativistic (� − 1 ≫ 1): Synchrotron radiation Non-thermal Transition from C’lotron to Synchrotron Emission 183 Thermal gyroresonance radiation • At a given B, thermal gyroresonance radiation is essentially a “spectral line” centered at Figiin? 6% Time �depednce�'", where of electric field from a particle of intemediate � = 1, 2, 3 … is the harmonic numberwfoci@in a magnetic jieU • Particularly relevant above active regions at microwave frequencies – Why? • Spectral width of a given resonance line o mXn ∆�/��'" ≈ 9 ,-' Very narrow in the corona (~1/3000) (h) • High opacity only at these “resonance layers”Figiin? 69b Power spectrum for a physical broadening mechanism occurs for a distribution of particle en- ergies; then the gyration frequency o, is proportional to l/y, so that the spectra of the particles do not fall on the same lines. Another effect that will cause the spectrum
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