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documentation fixes for spectral constraints #169

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Jan 5, 2025
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documentation fixes for spectral constraints #169

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16 changes: 8 additions & 8 deletions agnpy/constraints/spectral_constraints.py
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Original file line number Diff line number Diff line change
Expand Up @@ -34,23 +34,23 @@ def gamma_max_larmor(self):

.. math::

R_L < R_b \Rightarrow \gamma_{\mathrm{max}} < \frac{R_b e B}{m_e c^2}
R_L \u2264 R_b \Rightarrow \gamma_{\mathrm{max}} \u2264 \frac{R_b e B}{m_e c^2}
"""
return (self.blob.R_b * e * self.blob.B_cgs / mec2).to_value("")

@property
def gamma_max_ballistic(self):
r"""Naive estimation of maximum Lorentz factor of electrons comparing
acceleration time scale with ballistic time scale.
For the latter we assume that the particles crosses the blob radius.
For the latter we assume that the particles cross the blob radius.

.. math::

(\mathrm{d}E/\mathrm{d}t)_{\mathrm{acc}} &= \xi c E / R_L \\
T_{\mathrm{acc}} &= E \,/\,(\mathrm{d}E/\mathrm{d}t)_{\mathrm{acc}} = R_L / (\xi c) \\
T_{\mathrm{bal}} &= R_b / c \\
T_{\mathrm{acc}} &< T_{\mathrm{bal}}
\Rightarrow \gamma_{\mathrm{max}} < \frac{\xi R_b e B}{m_e c^2}
T_{\mathrm{acc}} \u2264 T_{\mathrm{bal}}
\Rightarrow \gamma_{\mathrm{max}} \u2264 \frac{\xi R_b e B}{m_e c^2}
"""
return self.blob.xi * self.gamma_max_larmor

Expand All @@ -63,7 +63,7 @@ def gamma_max_synch(self):
(\mathrm{d}E/\mathrm{d}t)_{\mathrm{acc}} &= \xi c E / R_L \\
(\mathrm{d}E/\mathrm{d}t)_{\mathrm{synch}} &= 4 / 3 \sigma_T c U_B \gamma^2 \\
(\mathrm{d}E/\mathrm{d}t)_{\mathrm{acc}} &= (\mathrm{d}E/\mathrm{d}t)_{\mathrm{synch}}
\Rightarrow \gamma_{\mathrm{max}} < \sqrt{\frac{6 \pi \xi e}{\sigma_T B}}
\Rightarrow \gamma_{\mathrm{max}} = \sqrt{\frac{6 \pi \xi e}{\sigma_T B}}
"""
return np.sqrt(
6 * np.pi * self.blob.xi * e / (sigma_T * self.blob.B_cgs)
Expand All @@ -77,9 +77,9 @@ def gamma_max_SSC(self):

.. math::
(\mathrm{d}E/\mathrm{d}t)_{\mathrm{acc}} &= \xi c E / R_L \\
(\mathrm{d}E/\mathrm{d}t)_{\mathrm{SSC}} &= 4 / 3 \sigma_T c U_{\mathrm{synch}} \gamma^2 \\
(\mathrm{d}E/\mathrm{d}t)_{\mathrm{SSC}} &= 4 / 3 \sigma_T c U_{\mathrm{SSC}} \gamma^2 \\
(\mathrm{d}E/\mathrm{d}t)_{\mathrm{acc}} &= (\mathrm{d}E/\mathrm{d}t)_{\mathrm{SSC}}
\Rightarrow \gamma_{\mathrm{max}} < \sqrt{\frac{3 \xi e B }{\sigma_T U_SSC}}
\Rightarrow \gamma_{\mathrm{max}} = \sqrt{\frac{3 \xi e B }{4 \sigma_T U_\mathrm{SSC}}}
"""
return np.sqrt(
3
Expand All @@ -95,7 +95,7 @@ def gamma_max_EC_DT(self, dt, r=0 * u.cm):
WARNING: assumes Thomson regime

.. math::
\gamma_{\mathrm{max}} = \sqrt{\frac{3 \xi e B }{ \sigma_T U'_\mathrm{ext}}}
\gamma_{\mathrm{max}} = \sqrt{\frac{3 \xi e B }{4 \sigma_T U'_\mathrm{ext}}}
"""
return np.sqrt(
3 * self.blob.xi * e * self.blob.B_cgs / (4 * sigma_T * dt.u(r, self.blob))
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