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**TRAYECTORIAS DE ELECTRONES A TRAVÉS DE LENTES MAGNÉTICAS**

DANIEL ANGOSTO & SERGIO CHAVES.

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

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

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DIPOLO MAGNÉTICO.

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**ESQUEMAS DE LENTES MAGNÉTICAS FORMADAS POR UN CUADRUPOLO MAGNÉTICO**

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FUERZA DE LORENTZ.

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**ESQUEMA DEL MICROSCOPIO.**

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**ESTRUCTURA DEL PROYECTO.**

Rungekutta.m LensSystem.m Lens.m DipoleField.m

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**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:

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**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.

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**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.

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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.

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RESULTADOS

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CONCLUSIONES

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**MUCHAS GRACIAS POR SU ATENCIÓN.**

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The magnetic force law (Lorentz law) The magnitude of the force is the B field x the perpendicular velocity x charge Or The velocity x the perpendicular.

The magnetic force law (Lorentz law) The magnitude of the force is the B field x the perpendicular velocity x charge Or The velocity x the perpendicular.

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