tokens: and potentially applicable for an empirical fitting of particle distribution function in various physical situations, it turns out that such a model has a fundamental significance in the context of the self-consistent Langmuir turbulence theory as discussed by Yoon ( 2012 , 2014 ). The purpose of the present paper is to reformulate the modified κ -model of Scherer et al. ( 2017 ) in light of the quasi-equilibrium of turbulent Langmuir fluctuation and the related electron κ -like distribution. That is, the present paper aims to show that the modified κ -model of Scherer et al. ( 2017 ) generalizes the model solution discussed by Yoon ( 2012 , 2014 ), thereby resolving the undesired feature of “infrared catastrophe” associated with the steady-state Langmuir turbulence spectral intensity. The organization of the present paper is as follows: Section 2 discusses the generalized theory of turbulent quasi-equilibrium between the Langmuir turbulence and suprathermal electron distribution, which leads to the regularized κ -model of Scherer et al. ( 2017 ). In the last section we discuss the physical origin of the exponential cutoff factor and also discuss the possible application of the present finding. 2. Equilibrium State between Langmuir Fluctuations and Electrons The fundamental aspect and details of the theory of the quasi-equilibrium state between Langmuir fluctuations and suprathermal electrons are already discussed elsewhere (Yoon 2012 , 2014 ; Livadiotis 2017 ), so we will not repeat the derivations of the equations here. Essentially, the theory boils down to three equations. The first equation represents the formal solution to the steady-state particle (electron) kinetic equation,where f e ( v ) represents the isotropic electron velocity distribution function; m e is the electron rest mass; I L ( k ) corresponds to the steady-state Langmuir fluctuation intensity, k being the magnitude of the wave number, which is being replaced by by virtue of the resonance condition; and is the plasma frequency, n and e being the ambient plasma number density and unit charge, respectively. The second equation is the steady-state wave kinetic equation for Langmuir fluctuations that are in linear wave–particle resonant interaction with the particles (electrons),whereis the Langmuir wave dispersion relation,being the electron thermal spread. Here, T e represents the Maxwellian temperature for the electrons. That is, T e is a macroscopic parameter had the electron distribution function been given by the Maxwellian distribution function. Of course, when the underlying distribution function is non-Maxwellian, then T e is not the real temperature, which is well known, and has also recently been systematically discussed by Nicolaou Livadiotis ( 2016 ). Consequently, by T e , we mean the electron temperature in a loose sense. The third equation represents the steady-state turbulent interaction between Langmuir fluctuations and thermal ions (protons), Of the
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