Characterization of linear quadrupoles operated with amplitude-asymmetric sinusoidal waveforms

The stability regions formed by the asymmetric sinusoidal shape of the periodic supply potential of the quadrupole mass filter are calculated, with the signal duty cycle <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>0.5</mml:mn></mml:math>. Two cases are considered, when <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>A</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo><</mml:mo><mml:mspace></mml:mspace><mml:msub><mml:mi>A</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>A</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>></mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>, where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>A</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>A</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> are the amplitudes of the positive and negative parts of the sinusoid. Stability islands are revealed, where the QMF operation is possible by changing amplitude <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>A</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> without DC potential. For the values <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>A</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>A</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn>0.8</mml:mn></mml:math>, the mass selected instability mode with a resolution of about 7000 is found. In this island, the potential well depth reaches its maximum along the <i>Y</i> coordinate. At the amplitudes <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>A</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>A</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn>1.8</mml:mn><mml:mo>-</mml:mo><mml:mn>2.0</mml:mn></mml:math>, stability regions are formed, the operation in which allows reaching <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>R</mml:mi><mml:mrow><mml:mn>0.5</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>2000</mml:mn></mml:math>. The results of the transmission and excitation contours modeling confirm the validity of the method for calculating the stability diagrams of a linear quadrupole with asymmetric sinusoidal waveform.