7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Energy exchange in a compact dipole plasma: thermodynamical investigations
through measurements and modeling
Ayesha Nanda, and Sudeep Bhattacharjee
Department of Physics, Indian Institute of Technology, Kanpur
e-mail (speaker): ayesha@iitk.ac.in
Temperature anisotropy prevails both in laboratory andastrophysical plasma. As a free energy source,
temperature anisotropy has revealed potential solutions toheating and particle acceleration issues, leading to thedisposal of heat in the form of energy. Energy conversion
for systems in local thermodynamic equilibrium has been
well understood. However, energy conversions in weakly
collisional or collisionless plasmas, which are far fromthermodynamic equilibrium, widely occurring inastrophysical environments, remains a forefront research
problem [1]. Several efforts have been put in recent years
to understand thermodynamics of plasma in terms oftheory [2] and simulation [1,3] in anisotropic magnetizedplasma. However, the thermodynamic potentials have notbeen explained in terms of plasma characteristic
parameters in plasma confined by dipole field. Therefore,
the current study seeks to develop a thermodynamic
relation that takes into account experimentally measured
parameters in response to plasma heating and energy loss
processes with varied operating pressure and power in a
dipole field.
The measurements will be carried out in a compact
dipole device [4] where several fundamental works suchas global plasma sustenance [5], diffusion induced
transport [6], optical emissions [7], temperature
anisotropy governed electrical conductivity [8] andcurrent density [9] have already been addressed. The
schematic of the device is shown in Fig. 1. Langmuirprobe and antenna probes for measurement of wave
electric fields, are employed for measurements at allaccessible spatial position (𝑟, 𝜃, 𝜙) with varying pressure(0.4, 1.2 and 2.0 mTorr) and input microwave power (300,350 and 400 W).

Fig. 1. Schematic of the experimental setup [9].
Initially, the local intrinsic entropy of our system wasobtained using Boltzmann’s H-theorem of kinetic theory
from electron energy distribution function [3], given by,𝑠 = ∑𝑗 𝑠𝑗 =316𝑛𝑘𝐵 {1 + 𝑙𝑛 (1/3 1/3 1/3𝑝𝜃 𝑝𝜙𝑛𝛾2𝜋 𝑝𝑟𝑚𝑒)}, (1)where, 𝑝𝑗 (= 𝑁𝑒 𝑘𝐵 𝑇𝑒𝑗 ) is the plasma pressure along 𝑗̂for 𝑗 → 𝑟, 𝜃 and 𝜙 , and 𝛾 is the adiabatic index. This
will be further disintegrated component wise as entropy
being a macroscopic quantity is additive in nature, which
will further aid to understand the heat added (Q) to thesystem from 2nd law of thermodynamics given by 𝑑𝑄𝑗 =𝑇𝑒𝑗 𝑑𝑠𝑗 + 𝑠𝑗 𝑑𝑇𝑒𝑗 along three directions. Furthermore, inan anisotropic magnetized plasma, the magnetic fieldhelps in interchange between parallel and perpendicularenergy, and provides additional work [3]. In the presenceof dipole field (B) it can be improvised as,𝑑𝑊 = ∑𝑗 𝑑𝑊𝑗 = (𝑝𝑟 𝑑𝑉 + 𝑝𝑟 𝑉𝑑𝐵𝐵) + (−𝑝𝜃 𝑉𝑉𝑘𝐵 𝑑(𝑛(𝑇𝑒𝑟 + 𝑑𝑇𝑒𝜃 + 𝑑𝑇𝑒𝜙 )),𝑑𝐵𝐵)+(2)where 𝑉 is the flux tube volume. This will help us todetermine change in internal energy from 1 st law ofthermodynamics: 𝑑𝑈𝑗 = 𝑑𝑄𝑗 − 𝑑𝑊𝑗 .
A mathematical power balance model is formulated tounderstand the energy transfer in plasma. In our case,microwave heating adds external heat to the plasma.
However, in dipole field, particles also gain energy bybetatron and Fermi heating [10] due to the mirror andcurvature drifts resulting in conservation of first andsecond adiabatic invariants respectively. The energy
dissipation happens through diffusion cooling, charge
exchange, inelastic and elastic collision, isotropizationand losses through the walls. The net energy retained fromthe abovementioned processes will modify 𝑑𝑈𝑗 .
The internal energy at every spatial location will beestimated from both the models to observe theiragreement with each other. Furthermore, otherthermodynamic potentials such as enthalpy, Helmholtz
free energy and Gibb’s free energy can be determined. In
the colloquium, results of the above-mentioned
investigation will be presented and the thermodynamics ofanisotropic magnetized plasma confined by a dipole field
will be discussed.
References[1] P. Cassak et al., Phys. Rev. Lett. 130, 085201 (2023).
[2] R. Hazeltine et al., Phys. Plasmas 20, 022506 (2013).
[3] S. Du et al., Phys. Rev. E 101, 033208 (2020).
[4] S. Bhattacharjee, A. R. Baitha, A. Nanda et al., Rev.
Mod. Plasma Phys. 6, 16 (2022).
[5] A. R. Baitha, A. Nanda et al., Plasma Res. Exp. 1,045005 (2019).
[6] A. R. Baitha, A. Nanda et al., AIP Adv. 10, 045328(2020).
[7] S. Bhattacharjee et al., Phys. Scr., 96 035605 (2021).
[8] A. Nanda et al., Phys. Plasmas 29, 062105 (2022).
[9] A. Nanda et al., Phys. Plasmas 30, 052107 (2023).
[10] Z. Zhong et al., Geophys. Res Lett 47 085141(2019).