Endoreversible Stirling cycles: plasma engines at maximal power

TL;DR

The paper analyzes endoreversible Stirling cycles with plasmas as the working medium, showing that if the caloric equation of state is linear in temperature and at most additive in volume, the efficiency at maximal power matches the Curzon-Ahlborn form $\eta_{CA}=1-\sqrt{\frac{T_c}{T_h}}$. This result holds for one-component plasmas (treated as modified ideal gases with $E=E_0+f\,T$) and extends to second-order virial corrections, including van der Waals-like behavior, indicating broad applicability beyond ideal gases. When the working medium is a relativistic electron-positron-photon plasma described by a photonic EOS $E=\epsilon V T^4$, the endoreversible efficiency becomes $\eta=\frac{1}{4}\big[1-(\frac{T_{c,p}}{T_{h,p}})^4\big]$, which is notably smaller and requires numerical optimization to assess maximal-power performance. The study highlights the robustness of CA efficiency for a large class of plasmas and contrasts the Stirling case with photonic media, offering a general framework for finite-time thermodynamics in plasma engines.

Abstract

Endoreversible engine cycles are a cornerstone of finite-time thermodynamics. We show that endoreversible Stirling engines operating with a one-component plasma as working medium run at maximal power output with the Curzon-Ahlborn efficiency. As a main result, we elucidate that this is actually a consequence of the fact that the caloric equation of state depends only linearly on temperature and only additively on volume. In particular, neither the exact form of the mechanical equation of state, nor the full fundamental relation are required. Thus, our findings immediately generalize to a larger class of working plasmas, far beyond simple ideal gases. In addition, we show that for plasmas described by the photonic equation of state the efficiency is significantly lower. This is in stark contrast to endoreversible Otto cycles, for which photonic engines have an efficiency larger than the Curzon-Ahlborn efficiency.

Figures (4)

• Figure 1: Schematic $PV$- and $TS$-diagrams of the Stirling cycle for the one-component plasma \ref{['eq:energy']} as a working medium.
• Figure 2: Schematic $PV$- and $TS$-diagrams of the Stirling cycle for the photonic gas \ref{['eq:energy_photo']} as a working medium.
• Figure 3: Endoreversible Stirling efficiency for the one-component plasma \ref{['eq:Curzon']} (blue line) and the photonic gas \ref{['eq:eta_photo']} (red line).
• Figure 4: Efficiency at maximal power for the photonic equation of state \ref{['eq:energy_photo']} (red line) together with the Curzon-Ahlborn efficiency \ref{['eq:Curzon']} (blue line), and the Carnot efficiency, $\eta_C=1-T_c/T_h$, (gray, dashed line). Parameters are $\alpha=1$, $\beta=1$, and $\gamma=1$.