Alkali metal ions such as Li+, Na+, and K+ play essential roles in agriculture, environmental monitoring, and education, yet their on-site quantification remains limited by the cost, size, and gas dependence of conventional instruments, including ICP-OES and flame photometers. In this study, we develop a compact, safe, and portable flame-less photometer that induces atomic emission via electrical excitation using a Tesla coil and detects spectral intensity with a miniature CCD spectrometer. To describe the nonlinear relationship between concentration and observed emission intensity, we derive a theoretical model incorporating self-absorption from the Radiative Transfer Equation and express it using effective parameters. Calibration experiments for Li+, Na+, and K+ demonstrate excellent agreement with the theoretical equation (R2 > 0.99), successfully capturing both near-linear behavior at low concentrations and saturation at high concentrations. Gaussian integration of spectral peaks and internal standardization improve the robustness of quantification. Furthermore, a two-point calibration method effectively corrects variations in instrument conditions, maintaining concentration estimation errors below 0.1 %. The device requires no fuel gas, operates on a mobile battery, and weighs only 75 g, enabling versatile use in agriculture (K+ fertilization management, Na+ salinity assessment), environmental analysis, and educational settings. These results establish a practical and accessible platform for multi-element alkali metal ion quantification.