Accelerating voltage

In electron and ion optics , an acceleration voltage is applied between electrodes to give electrically charged particles kinetic energy . The electric field strength between the electrodes and thus the acceleration of the particles depend on the distance between the electrodes, but the increase in energy at the end of the acceleration path does not (see potential and voltage ), hence the importance of the acceleration voltage and the specification of particle energies in the unit electron volts . Relativistic speeds are achieved with easily manageable voltages .

Energy and speed

Particles of the charge receive electrical energy through an accelerating voltage ${\ displaystyle q}$ ${\ displaystyle U}$

{\ displaystyle E _ {\ mathrm {el}} = qU,}

For non-relativistic velocities ( ) the kinetic energy of a particle is approximately the mass ${\ displaystyle v \ ll c}$ ${\ displaystyle m}$

{\ displaystyle E _ {\ mathrm {kin}} \ approx {\ frac {1} {2}} mv ^ {2}.}

Equating results

{\ displaystyle v = {\ sqrt {2U {\ frac {q} {m}}}}}

Calculation example: The specific charge of the electron is about so that an acceleration voltage of −2.84 volts is sufficient for a speed of 1000 km / s. ${\ displaystyle {\ frac {-e} {m _ {\ mathrm {e}}}}}$ ${\ displaystyle -1 {,} 76 \ cdot 10 ^ {11} \, \ mathrm {\ frac {C} {kg}},}$

For the exact relationship between speed and energy see kinetic energy in relativistic mechanics .

The reasons for choosing the accelerating voltage can relate to a number of parameters:

Velocity: Drift through the quadrupole in the case of a quadrupole mass spectrometer .
De Broglie wavelength : with about 100 eV matching the lattice constant in low-energy electron diffraction , with about 200 kV as short-wave as possible with the transmission electron microscope .
Energy: with a few 10 to a few 100 keV in X-ray tubes for X-ray energies matched to the sample or with a few 10 MeV as high as possible for high resolution in radiocarbon dating .
Penetration depth of ions: below 500 eV for sputtering , 500 eV to a few MeV for ion implantation .
Picture display in picture tubes: In picture tubes of color televisions, an accelerating voltage of 25 to 30 kV ensures that even a small current of electrons makes the luminous layer shine brightly. Low current at high airspeed means a low space charge, so that the focus is little affected.