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ω lhr = 1 2 ω c e 2 + ω c i 2 + ω p e 2 + ω p i 2 − ( ω c e 2 − ω c i 2 + ω p e 2 ) 2 + 2 ( − ω c e 2 + ω c i 2 + ω p e 2 ) ω p i 2 + ω p i 4 {\displaystyle \omega _{\text{lhr}}={\frac {1}{\sqrt {2}}}{\sqrt {\omega _{ce}^{2}+\omega _{ci}^{2}+\omega _{pe}^{2}+\omega _{pi}^{2}-{\sqrt {\left(\omega _{ce}^{2}-\omega _{ci}^{2}+\omega _{pe}^{2}\right)^{2}+2(-\omega _{ce}^{2}+\omega _{ci}^{2}+\omega _{pe}^{2})\omega _{pi}^{2}+\omega _{pi}^{4}}}}}}
