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TRAYECTORIAS DE ELECTRONES A TRAVÉS DE LENTES MAGNÉTICAS DANIEL ANGOSTO & SERGIO CHAVES.

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Presentation on theme: "TRAYECTORIAS DE ELECTRONES A TRAVÉS DE LENTES MAGNÉTICAS DANIEL ANGOSTO & SERGIO CHAVES."— Presentation transcript:

1 TRAYECTORIAS DE ELECTRONES A TRAVÉS DE LENTES MAGNÉTICAS DANIEL ANGOSTO & SERGIO CHAVES.

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

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

4 DIPOLO MAGNÉTICO.

5 LENTES MAGNÉTICAS. ESQUEMAS DE LENTES MAGNÉTICAS FORMADAS POR UN CUADRUPOLO MAGNÉTICO

6 FUERZA DE LORENTZ.

7 ESQUEMA DEL MICROSCOPIO.

8 ESTRUCTURA DEL PROYECTO. Rungekutta.m LensSystem.m Lens.m DipoleField.m

9 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:

10 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.

11 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.

12 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.

13 RESULTADOS

14 CONCLUSIONES

15 MUCHAS GRACIAS POR SU ATENCIÓN.


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