r"""
Petschek vs. Sweet-Parker reconnection
===========================================

Harry Petschek (1964) proposed a resolution to the Sweet-Parker
rate problem (:doc:`plot_02_sweet_parker_reconnection`): if the
resistive diffusion region shrinks to a small X-point rather than
extending the full length of the current sheet, four standing
slow-mode shocks radiating from that X-point can carry away most of
the inflowing magnetic flux and energy. The resulting reconnection
rate falls only *logarithmically* with the Lundquist number,
:math:`v_{in}/v_A\approx\pi/(8\ln S)`, fast enough to plausibly explain
solar flare and magnetospheric substorm energy-release timescales that
Sweet-Parker reconnection could not.

:func:`~physicskit.plasma.mhd.petschek_rate` -- compare directly
against :func:`~physicskit.plasma.mhd.sweet_parker_rate` at the same
Lundquist number to see the difference explode as :math:`S` grows.
"""

# %%
import matplotlib.pyplot as plt
import numpy as np

import physicskit as pk

# %%
# Compare the two reconnection rates across the same S range
# ------------------------------------------------------------------
# From laboratory to solar-flare-scale Lundquist numbers, Sweet-Parker's
# S^(-1/2) collapses toward zero while Petschek's logarithmic
# pi/(8 ln S) stays observationally plausible.

S_vals = np.logspace(4, 14, 50)
sp_rate = np.array([pk.plasma.sweet_parker_rate(S) for S in S_vals])
pet_rate = np.array([pk.plasma.petschek_rate(S) for S in S_vals])

fig, axes = plt.subplots(1, 2, figsize=(10, 4))
axes[0].loglog(S_vals, sp_rate, label=r"Sweet-Parker $S^{-1/2}$")
axes[0].loglog(S_vals, pet_rate, label=r"Petschek $\pi/(8\ln S)$")
axes[0].axvline(1e12, color="gray", linestyle="--", linewidth=0.8, label="solar flare S")
axes[0].set_xlabel("Lundquist number S")
axes[0].set_ylabel(r"reconnection rate $v_{in}/v_A$")
axes[0].set_title("Petschek's logarithmic rate vs. Sweet-Parker's S^(-1/2)")
axes[0].legend()

# %%
# How far apart the two predictions actually are
# ------------------------------------------------------------------------
# Overlaid on a log-log rate axis, the two curves' separation is easy to
# underestimate; plotting their ratio directly shows Petschek's rate
# pulling ahead by many orders of magnitude precisely where it matters --
# solar-flare-scale Lundquist numbers.

ratio = pet_rate / sp_rate
axes[1].semilogy(S_vals, ratio, color="darkorange")
axes[1].axvline(1e12, color="gray", linestyle="--", linewidth=0.8)
s_flare_idx = np.argmin(np.abs(S_vals - 1e12))
axes[1].annotate(f"{ratio[s_flare_idx]:.0e}x at solar-flare S", (S_vals[s_flare_idx], ratio[s_flare_idx]))
axes[1].set_xscale("log")
axes[1].set_xlabel("Lundquist number S")
axes[1].set_ylabel(r"Petschek rate / Sweet-Parker rate")
axes[1].set_title("The reconnection-rate gap, made explicit")
fig.tight_layout()

plt.show()