  (), Amir Levinson, Benoit Cerutti

GRMHD Numerical Simulations
Artificial mass supply
in the jet region.

Porth+ 17

Predictions of the jet emission
are highly uncertain.
EHT Coll. 19

TeV flare from radio galaxy
Aleksić+ 14

IC310

Flux doubling timescale < 4.8 min at 95% C.L.
corresponds to ~20% of the timescale rg/c.

→ Particle acceleration at sub-horizon scale?

Electromagnetic Cascadee.g., Beskin+ 92

B-field

B-field

Jet
Disk

Plasma injection mechanism
without external plasma inflow
and external high-energy photons.

e+E-field E||

Electromagnetic Cascadee.g., Beskin+ 92

B-field

B-field

Jet

γr

ay

Disk

Plasma injection mechanism
without external plasma inflow
and external high-energy photons.

e+E-field E||

Electromagnetic Cascadee.g., Beskin+ 92

B-field

B-field

Jet
Disk

γr

ay

e- e+

Plasma injection mechanism
without external plasma inflow
and external high-energy photons.

DiskemissionE-field E||e+Electromagnetic Cascadee.g., Beskin+ 92

B-field

B-field

e- e+

Jet

γr

ay

Disk

e- e+

Plasma injection mechanism
without external plasma inflow
and external high-energy photons.

e- e+

Disk
emissionE-field E||e+Electromagnetic Cascadee.g., Beskin+ 92

B-field

B-field

Jet

- +
e
e
e e+

γ
-r

ay

Disk

e- e+

Plasma injection mechanism
without external plasma inflow
and external high-energy photons.

e- e+

e- e+
Disk
emissionE-field E||e+

1D PIC Model

Levinson & Cerutti 18

1-dimensional structure: the gap extends along a poloidal
magnetic surface as a function of θ.
→ Ignoring any MHD waves, considering only plasma oscillations.
The gap constitutes a small disturbance.
→ The activity does not significantly affect the global structure(the B-field geometry and the angular velocity).
Isotropic radiation field (from accretion disk) for seed photons.
Is (xµ , ✏s , ⌦s ) = I0 (✏s /✏s,min ) p , ✏s,min < ✏s < ✏s,max<latexit sha1_base64="lmetd4vlEqKOcwA986LF4HllJGU=">AAAC43ichVFLSxtRFD4zrdWmD+NjIbgJDSkRYjwjgkUUBDe6qq9EwUmGmfEmXpwXcydBHSY/oO5EcCEuWihF/Bnd9A904b4b6dJCNy56MhkaNNieYe797ved79xz7zU8i4sA8VqSnzzte9Y/8Dz14uWr14PpoeGycBu+yUqma7n+tqELZnGHlQIeWGzb85luGxbbMvaX2vpWk/mCu85mcOixiq3XHV7jph4QpaVbK5rIH1RD1W5EBZV5gltEi0KoGrWM+t5mdT3SxMTCiob5rjz1F4aioNrciSaq4aQXFVqtHmW+a5u/L+oHkZbOYhHjyPQCJQFZSGLVTX8BFXbBBRMaYAMDBwLCFugg6NsBBRA84ioQEucT4rHOIIIUeRuUxShDJ3afxjqtdhLWoXW7pojdJu1i0e+TMwM5/I6XeIvf8Apv8O7RWmFco93LIc1Gx8s8bfDD2Mbv/7psmgPY67r+2XMANXgX98qpdy9m2qcwO/7m0dntxtx6LnyLn/An9f8Rr/ErncBp/jI/r7H1c0jRAygPr7sXlKeLChaVtZns4nTyFAMwDm8gT/c9C4uwDKtQon1/SClpRBqVmXwsn8innVRZSjwjcC/kiz8mV7sQ</latexit>

JJNo external plasma source.
The global current is a free parameter.
A split monopole geometry for the global B-field.
The angular velocity of magnetic surface ⌦ = 0.5!H.
<latexit sha1_base64="FIoUPIjigMef9owCiuTmcOKdS1Y=">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</latexit>

Calculation
domainAccretion disk

Background spacetime
Kerr metric given in BL coordinates

Tortoise coordinate

Basic equations
Gauss’s law

@µ (

p

tµ

gF ) = (<latexit sha1_base64="N1X74V0f0MWF/Az8RZpSqX3EkYM=">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</latexit>→
Contour of ρGJ
Null charge
surface

Levinson & Segev 17p

gj t )

Levinson & Cerutti 18

Basic equations
Gauss’s law

@µ (

p

tµ

gF ) = (p

gj t )<latexit sha1_base64="N1X74V0f0MWF/Az8RZpSqX3EkYM=">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</latexit>→
Ampère’s law(radial component)
p
p
rµ
@µ (
gF ) = (gj r )
J0<latexit sha1_base64="AgJ6bwpTR7oX5FG8RnxI1mj62zI=">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</latexit>→

J0

Calculation
domainLevinson & Cerutti 18

Basic equations
Equation of motion for i-th particle<latexit sha1_base64="YNfn5NADB75bh7fbudUCF8oCZx8=">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</latexit>

→

→

duµi
=
d⌧i

Levinson & Cerutti 18

Curvature
loss termqi µ ↵
µ
µ
↵
u
u
+
F
u
+
s
i i
i
↵
me ↵ i

Basic equations
Equation of motion for i-th photon

IC scattering Z r(t+ t)p⌧sc =KN grr drPair productionr(t)<latexit sha1_base64="i9tSpXki6ARZiA0Ownr8+KnDtAw=">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</latexit>⌧pp =Z r(t+ t)r(t)<latexit sha1_base64="BzW47skZSXjdGQnRVSL+Usery2g=">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</latexit>ppp grr drLevinson & Cerutti 18

Parameters
Fiducial optical depth
Global current density
BH mass⌧0 = 4⇡rg T I0 /hc = 10<latexit sha1_base64="7es2BXSEM4+fZ6wCm0/3Lowwo0o=">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</latexit><latexit sha1_base64="dRplEZi2J+bB7UGygc7q7vc/h6g=">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</latexit>

j0 = 1.0

MBH = 109 M<latexit sha1_base64="yj+x93+Bd2Pg9CN9GJXEW4upgOw=">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</latexit>

Dimensionless spin parameter
B-field on the horizona⇤ = 0.9<latexit sha1_base64="7pkSPR3yLhTFxxUbB34q9sx+hxs=">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</latexit>

BH = 2⇡ ⇥ 103 G<latexit sha1_base64="qGLvhoDG2L+K6+MvQYCL0xMn5Ik=">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</latexit>

Inclination angle of magnetic surface ✓ = 30
<latexit sha1_base64="xkSxiV2i8YKbWbqQnFcyl/mnZyc=">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</latexit>

Minimum energy of seed photon✏s,min = 10 8 me c2<latexit sha1_base64="gLp3/weJz/rQDBt66QrOP0nQ4fQ=">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</latexit>

Slope of seed photon spectrum<latexit sha1_base64="+TNu6rz/LEN/BrAEtzRtKSQ6R78=">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</latexit>

Curvature radius

p=2

Rcur = rg<latexit sha1_base64="oulvWjdZj07gxoLd4x9xfLyqing=">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</latexit>

Number of cells
N = 32768
rg
M9 BH,3
3
&
⇠ 10
lp
< 8>
<latexit sha1_base64="PVE3DMrfheXp/Tcmf3TVFWtudEQ=">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</latexit><latexit sha1_base64="xtV5sYzSMyTyvjBQaAvqesrfTcM=">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</latexit>

We neglect the scattering of particles with < 107 .
<latexit sha1_base64="VS0Uvahj7ogdlb8XOd3fI4JH7NU=">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</latexit>

Pair multiplicity in gap

Pairs quickly accelerate to the terminal Lorentz factor in the gap.

eEk = Prad /c<latexit sha1_base64="DSuLl3oSFxKW8vF5D8ZKHISU/H8=">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</latexit><latexit sha1_base64="JnaEUpJFpgJS+fNaV/EJwx1ipa0=">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</latexit>

10
⇠
10
max

⌧0 = 4⇡rg T I0 /hc =<latexit sha1_base64="7es2BXSEM4+fZ6wCm0/3Lowwo0o=">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</latexit>

Minimum energyof soft photons✏min = 10 9 me c2

Scattering opticaldepth (KN)⌧IC /⌧0 ⇠ O(10 1 )Pair creation
optical depth⌧ /⌧0 ⇠ O(10 1 )<latexit sha1_base64="qPwIzs65cTgL8izM4OuSy7UpPQM=">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</latexit><latexit sha1_base64="iHiH2zCg1pV+rRHSkNxHGgsR+Tk=">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</latexit><latexit sha1_base64="U/es8zV3aDxkgfic7cN+VmC4GRM=">AAACjnicSyrIySwuMTC4ycjEzMLKxs7BycXNw8vHLyAoFFacX1qUnBqanJ+TXxSRlFicmpOZlxpaklmSkxpRUJSamJuUkxqelO0Mkg8vSy0qzszPCympLEiNzU1Mz8tMy0xOLAEKxQtoxpQklsZXx6Qn5uYmQshafbCYQUxxZq6Cv4ahQVy1rmGtZryAsoGeARgoYDIMoQxlBigIyBdYzhDDkMKQz5DMUMqQy5DKkMdQAmTnMCQyFANhNIMhgwFDAVAslqEaKFYEZGWC5VMZahm4gHpLgapSgSoSgaLZQDIdyIuGiuYB+SAzi8G6k4G25ABxEVCnAoOqwVWDlQafDU4YrDZ4afAHp1nVYDNAbqkE0kkQvakF8fxdEsHfCerKBdIlDBkIXXjdXMKQxmABdmsm0O0FYBGQL5Ih+suqpn8OtgpSrVYzWGTwGuj+hQY3DQ4DfZBX9iV5aWBq0GwGLmAEGKIHNyYjzEjP0FjPKNBE2cEGGhUcDNIMSgwawPA2Z3Bg8GAIYAgF2tvPsJVhH8N+JgEmMyZbJnuIUiZGqB5hBhTA5AEAtZuY2Q==</latexit>

Pair multiplicity
in the gap

O(10 2 ) ⇥ ⌧0<latexit sha1_base64="Hb/HX8Pu2gmY2CDAckQ/Ay8LjsM=">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</latexit>

cf. Levinson & Cerutti 18✏min = 10 8 me c2⌧0 = 10<latexit sha1_base64="/AgUIj+53PFQR7YrOBM3EEkBeyY=">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</latexit>✏min = 10<latexit sha1_base64="qPwIzs65cTgL8izM4OuSy7UpPQM=">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</latexit>

9

me c

2 → ⌧
<latexit sha1_base64="QsztMO4bFapNijmwZBjcAjsI4so=">AAACdXichVHLLgRBFD3T3uPV2EhEIgaxGrc9QsRCYmM5g0FiZNLdyuhMv9JdM8mY+AE/YMGGBBGfYeMHLHyCWJLYWLjT04kguJWqOnXqnlunqgzftkJJ9JhQmppbWtvaO5KdXd09vWpf/2bolQNT5EzP9oJtQw+FbbkiJy1pi20/ELpj2GLLKK3U97cqIggtz92QVV/sOnrRtfYtU5dMFVQ1L/VygfJFyTmORlRQU5SmKEZ+Ai0GKcSR8dRr5LEHDybKcCDgQjK2oSPktgMNBJ+5XdSYCxhZ0b7AEZKsLXOW4Ayd2RKPRV7txKzL63rNMFKbfIrNPWDlCMbpgW7ohe7plp7o/ddatahG3UuVZ6OhFX6h93hw/e1flcOzxMGn6k/PEvtYiLxa7N2PmPotzIa+cnjysr64Nl6boAt6Zv/n9Eh3fAO38mpeZsXaKZL8Adr35/4JNqfT2kx6LjubWl6Kv6IdQxjFJL/3PJaxigxyfG4FZ7jEVeJNGVbGlIlGqpKINQP4EsrUB14AkAA=</latexit>

0 & 100<latexit sha1_base64="ycdH9PqE3dJxfWNUmLPc3lKNnDE=">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</latexit>

Muitiplicity O(10-3)

Electric Currents
Polar region: J0 < 0Equatorial region : J0 > 0J0 < 0J0 > 0<latexit sha1_base64="ckO8SDdhsBQVGJ25ZHJPqUa1MrM=">AAACcHichVHLSsNAFD2N7/qquim4sFoqIhpufKCIguDGpa+qUEtJ4lSjaRKTtFCLP+APuHCjgoj4GW78ARd+grhTwY0Lb9OAqKh3mJkzZ+65c2ZGc0zD84keIlJdfUNjU3NLtLWtvaMz1tW97tlFVxdp3TZtd1NTPWEalkj7hm+KTccVakEzxYa2v1Dd3ygJ1zNsa80vOyJbUHcsI2/oqs9Udi9Hc6OKTCMJHnKxJMkUROInUEKQRBhLduwKW9iGDR1FFCBgwWdsQoXHLQMFBIe5LCrMuYyMYF/gCFHWFjlLcIbK7D6PO7zKhKzF62pNL1DrfIrJ3WVlAim6p2t6oTu6oUd6/7VWJahR9VLmWatphZPrPI6vvv2rKvDsY/dT9adnH3lMB14N9u4ETPUWek1fOjx5WZ1ZSVUG6YKe2P85PdAt38AqveqXy2LlFFH+AOX7c/8E62OyMi5PLk8k52fDr2hGLwYwxO89hXksYglpPvcAJzjDeeRZikt9Un8tVYqEmh58CWn4A3WkjMY=</latexit>

j0 =1.0, 1.0

Blandford & Znajek 77

Results

j0 = -1.0

Quasi-periodic oscillation
10

Numberdensity 10<latexit sha1_base64="1JGeeOYsPdZSo8jp7t8DRsk1CzY=">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</latexit>

τ0 = 300
Current
density0(n/nGJ )⌃j r /|J0 |<latexit sha1_base64="Ao8yAmBFSPjMoHqGHhLOBJRyl3s=">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</latexit>

0
1.5
E-field 0.001
pp
AEr / AH BH 0

-10
r/rg

4.0

1.5
10

r/rg

Energyspectrum<latexit sha1_base64="viblkAstBv8a1gAFhUX5790G8hk=">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</latexit>-0.001

u2

10-2-0.002
1.5

4.0

r/rg

4.0

<latexit sha1_base64="ieBtQ9/rNH+1D8ls1jJA2PyDk8Q=">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</latexit>

106

Null charge
surface (ρGJ=0)

108
u

1010

dN
du

j0 = -1.0

Results

Quasi-periodic oscillation
10

Numberdensity 20<latexit sha1_base64="1JGeeOYsPdZSo8jp7t8DRsk1CzY=">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</latexit>

τ0 = 100
Current
density0(n/nGJ )⌃j r /|J0 |<latexit sha1_base64="Ao8yAmBFSPjMoHqGHhLOBJRyl3s=">AAACdXichVHLLgRBFD3TXmO8GhuJSCYGsRp3GCFWEhuxwhgkHpPuVkbRr3T3TMLwA37Agg0JIj7Dxg9Y+ASxJLGxcKenE0FwK1V16tQ9t05V6a4p/YDoMabU1Tc0NsWbEy2tbe0damfXsu+UPEPkDcd0vFVd84UpbZEPZGCKVdcTmqWbYkXfm6nur5SF50vHXgr2XbFhaUVbbktDC5gqqOp6ThYtLbm76Y0czhXosKCmKE1hJH+CTARSiGLeUa+xji04MFCCBQEbAWMTGnxua8iA4DK3gQpzHiMZ7gscIcHaEmcJztCY3eOxyKu1iLV5Xa3ph2qDTzG5e6xMYpAe6IZe6J5u6Ynef61VCWtUvezzrNe0wi10HPfk3v5VWTwH2PlU/ek5wDYmQ6+SvbshU72FUdOXD05eclOLg5UhuqBn9n9Oj3THN7DLr8blglg8RYI/IPP9uX+C5dF0Ziw9vpBNTWejr4ijF/0Y5veewDRmMY88n1vGGS5xFXtT+pQBZaiWqsQiTTe+hDLyATZbj+c=</latexit>

0
1.5
E-field 0.005pp
AEr / AH BH 0

-10
r/rg

4.0

1.5

r/rg

Energyspectrum1<latexit sha1_base64="viblkAstBv8a1gAFhUX5790G8hk=">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</latexit>

10-2

-0.01

-0.02
1.5

4.0

u2
<latexit sha1_base64="ieBtQ9/rNH+1D8ls1jJA2PyDk8Q=">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</latexit>

r/rg

4.0

106

Null charge
surface (ρGJ=0)

108
u

1010

dN
du

Acceleration model

For simplicity, GR effects
are neglected.

Considering the gap until the pair formation front.

Electric field

Lorentz factorr · Ek = 4⇡(⇢e ⇢GJ )→ Ek = 2⌦B⇠x/c<latexit sha1_base64="q4zpMLHNimqxutLq/bWueV6jASM=">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</latexit><latexit sha1_base64="/hSwfQQCqEzqAGQcSLmxcVARCmk=">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</latexit>γ

Gap width : Δ
Pair formation
front

Pcur
c

Gap width : Δ<latexit sha1_base64="bye1+Ea78iOSoWZUBnaOwUlMxmQ=">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</latexit>

E||

PIC
c

d( me c)= eEk
dt<latexit sha1_base64="P/4ILK9KyFd2HqOtJQ7nu29zjxc=">AAACg3ichVG7SgNBFD2u7/iK2giCBIMiCPEmCoogBIKgXXxEBSNhdx3j4uyD3U1AQzorf8DCSkFELfUPbPwBCz9BLBVsLLzZLIiKeoeZOXPmnjtnZjRHGp5P9NigNDY1t7S2tUc6Oru6e6K9fWueXXJ1kdNtabsbmuoJaVgi5xu+FBuOK1RTk2Jd28vU9tfLwvUM21r19x2xZapFy9gxdNVnqhAdEvOFSt5RXVVKIav5YjGWZcI1Y4uZ6oReiMYpQUHEfoJkCOIII2tHL5DHNmzoKMGEgAWfsYQKj9smkiA4zG2hwpzLyAj2BaqIsLbEWYIzVGb3eCzyajNkLV7XanqBWudTJHeXlTGM0ANd0gvd0zU90fuvtSpBjZqXfZ61ulY4hZ6jgZW3f1Umzz52P1V/evaxg5nAq8HenYCp3UKv68sHxy8rs8sjlVE6o2f2f0qPdMc3sMqv+vmSWD5BhD8g+f25f4K1VCI5mUgtTcXTFH5FGwYxjDF+72mksYAscnzuIa5wg1ulWRlXUspUPVVpCDX9+BLK3Adz/ZTa</latexit>eEk

PIC /cxacc

eEk ' PIC /c<latexit sha1_base64="qMlHa47w5eYvkQRwYCzaPkTR4rI=">AAAChnichVHLSiNBFD22j4nxFXUz4CZOUFzFG0dRXAXCwLiLj6hgJHS3pRZWP+zuBGLIWvAHXLhyQETErX6AG3/AhZ8gs1Rw48KbToOoqLeoqlOn7rl1qspwlfQDorsWrbWtveNHrDPe1d3T25foH1j2nbJnioLpKMdbNXRfKGmLQiADJVZdT+iWocSKsZNr7K9UhOdLx14Kqq5Yt/QtW25KUw+YKiWGxZ9Srejqnq6UUPWiLy2xm8wz51nJuVx93CwlUpSmMJIfQSYCKUSRdxKnKGIDDkyUYUHARsBYQYfPbQ0ZEFzm1lFjzmMkw32BOuKsLXOW4Ayd2R0et3i1FrE2rxs1/VBt8imKu8fKJEbols7ogW7onO7p+dNatbBGw0uVZ6OpFW6p7+Dn4tO3KovnANuvqi89B9jETOhVsnc3ZBq3MJv6yt7hw+LswkhtlP7Rf/Z/THd0zTewK4/mybxYOEKcPyDz/rk/guWJdOZ3emJ+MpWl6CtiGMIvjPF7TyOLv8ijwOfu4wKXuNJiWlqb0qabqVpLpBnEm9CyL65plkk=</latexit>

xacc + xγ

x<latexit sha1_base64="BLanb70FFc0QDUpy8Ztr34+noQE=">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</latexit>x⇢e )/⇢GJ , ⇢GJ ⇠ ⌦B/(2⇡c)⇠ ⌘ (⇢GJ<latexit sha1_base64="E4b7rgIsJwOg/KvJqvPROYjsjks=">AAACh3ichVFNLwNBGH66PltfxUXismlDuNS0BHEqDsRFfRSJlWZ3jZrYr+xum9D0Lv6AgxOJiEhcubv4Aw5+gjiSuDh4u91EELyTmXnmmfd555kZzTGE5zP2GJEaGpuaW1qjsbb2js6ueHfPmmeXXJ3ndduw3Q1N9bghLJ73hW/wDcflqqkZfF3bm63tr5e56wnbWvX3Hb5lqkVL7Ahd9YkqxBOKu2sXKoprynMLVcUTprJo8qIqz4wMZRRHyPpwIZ5kKRaE/BOkQ5BEGDk7fgEF27ChowQTHBZ8wgZUeNQ2kQaDQ9wWKsS5hESwz1FFjLQlyuKUoRK7R2ORVpsha9G6VtML1DqdYlB3SSljgD2wS/bC7tkVe2Lvv9aqBDVqXvZp1upa7hS6jvpW3v5VmTT72P1U/enZxw4mA6+CvDsBU7uFXteXD45fVqaWByqD7Iw9k/9T9sju6AZW+VU/X+LLJ4jRB6S/P/dPsJZJpUdTmaWxZHYs/IpW9COBIXrvCWQxjxzydO4hrnGDWykqjUjj0mQ9VYqEml58CWn6A0gklZA=</latexit>

Gap width Δ is the minimum value of the sum of
the acceleration length xacc(γ) and the mean free path xγ(γ).

→<latexit sha1_base64="JDm+Y3/ruTQXwzfZwpmylnUO75k=">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</latexit>/rg ⇠ 9 ⇥ 10

3

1
3

1
3

1
3

1
3

1
3

⌧2 ✏min, 9 a0.9 B4 M9 ⇠
1
3

1
3

2
3

B2 ⌘ B/102 G<latexit sha1_base64="u+bMcT13Ej8QoWYf01io5IJ9Gdg=">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</latexit>

1
3→ Ek /B ⇠ 2⇠a /rg ⇠ 2 ⇥ 10 ⌧2 ✏min, 9 a0.9 B2 M9 ⇠2<latexit sha1_base64="eQtIovoxfaEc/MyjqrjF0z6zW7E=">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</latexit>

2
3

Summary

We perform 1D GRPIC simulation for pair cascadein the black hole magnetosphere.