TRAYECTORIAS DE ELECTRONES A

TRAVÉS DE LENTES MAGNÉTICAS

DANIEL ANGOSTO & SERGIO CHAVES.

INTRODUCCIÓN

• Simulación del comportamiento de electrones en presencia de un campo magnético generado por las lentes magnéticas de un microscopio electrónico de barrido.

EL MICROSCOPIO.

ESQUEMA DEL FUNCIONAMIENTO DE UN MICROSCOPIO ÓPTICO (IZDA.), UN MICROCOPIO ELECTRÓNICO DE TRANSMISIÓN (CENTRO)Y UN MICROCOPIO

ELECTRÓNICO DE BARRIDO (DCHA.).

DIPOLO MAGNÉTICO.

LENTES MAGNÉTICAS.

ESQUEMAS DE LENTES MAGNÉTICAS FORMADAS POR UN CUADRUPOLO MAGNÉTICO

FUERZA DE LORENTZ.

ESQUEMA DEL MICROSCOPIO.

ESTRUCTURA DEL PROYECTO.Rungekutta.m

LensSystem.m

Lens.m

DipoleField.m

LensSystem.m

• function B = lensSystem(R,MUT,Z,nl,r)

• % This function calculates the magnetic field at several points calling the• % function lens three times. The system is going to be composed by three• % magnetic lens located at a distance z1, z2, z3 from the origin. • % Input: • % R: Radius of the lens, in m.• % Mut: Dipole moment given as a matrix 4xn in which 4 rows defines the dipolar

moment of a every lens, in T*m^2.• % Z: Distance from the origin, given as a vector 1xn, in m.• % r: Matrix of nx3 dimensions in which the magnetic field is going to be• % calculated, in m.• % nl: Number of lens that form the system.• % Output:

Lens.m

• function B= lens( R, mu, z, r)• % This function calculates the magnetic field created by a quadrupole• % magnetic, which is formed by 4 dipoles. It?s needed a matrix mu, formed• % by 4 magnetic moments and the distance between the origin and every• % dipole, generated by z+R.• % Input:• % R: Distance from the centre of the dipole to each dipole (radius), in m.• % mu: Matrix(4x3) with the magnetic moment of 4 dipoles, in m^2*A.• % z: Distance from the origin to the centre of the lens, in m.• % r: Vector from the origin to an arbitrary point, in m.

DipoleField.m• function B = DipoleField( mu, rmu, r )• % This function calculates the magnetic field created by a dipole,

given• % the dipole moment, the distance between the dipole and the

origin, and• % the distance r from the origin to an arbitrary point r.• % Input: Everything in 3D.• % mu: Dipole moment, in m^2 * A.• % rmu: Distance between the origin and the dipole, in m.• % r: Distance between the origin and a point r, in m.• % Output:• % B: Magnetic field at a point, in T.

FLORENTZ• % This function calculates the force on a particle created by the

action of• % a Magnetic Field, in our case, the particles are electrons.• % The form of the force is F= q*vxB, where q is the charge in C, v the• % speed, in m/s and B is the Magnetic Field in T.• % Input:• % v: Speed of the particle, we are supposing it constant, in m/s.• % r: Matrix of nx3 dimensions in which the magnetic field is going to

be• % calculated calling lensSystem, in m.• % Output:• % F: Force suffered by the particle, in N.

RESULTADOS

CONCLUSIONES

MUCHAS GRACIAS

POR SU ATENCIÓN.