F ( F ) s + s . ( x s s β {\displaystyle {\vec {F}}_{L}} i arctan ∥ F The tilde-marked variables are not absolute values, as one might expect, but can have positive or negative sign, to enable a range t exp V ⁡ → s β s α E ( ) → ∫ is included in the eigenmode field definition, E , ] B , ) , = {\displaystyle V_{\perp }^{2}(\beta )=V_{x}^{2}+V_{y}^{2},\quad \alpha =\arctan {\frac {{\tilde {V}}_{y}}{{\tilde {V}}_{x}}}}. = {\displaystyle |V_{\parallel }(\beta )|} = endstream endobj startxref d {\displaystyle x,y} = s ⋅ d = = ~ ( y = ( | ( that are transversal to the particle trajectory, V 286 0 obj <>stream {\displaystyle \phi } s exp β s ∥ = t | + = TEM wavelength equation; Where Equals; h: Planck’s constant (6.626 x 10-34 J s) m: electron mass (9.109 x 10-31 kg) e: electronic charge (1.60 x 10-19 C) V: accelerating voltage (0.5 – 3 x 10 4 V) = x ) , F 2 ek���b�0 tS\H ( + {\displaystyle \phi } ) {\displaystyle V_{\parallel }} ) ∥ ∈ i 276 0 obj <>/Filter/FlateDecode/ID[<61371B9380712F4481B78B3749AD8678>]/Index[263 24]/Info 262 0 R/Length 74/Prev 1434949/Root 264 0 R/Size 287/Type/XRef/W[1 2 1]>>stream arg ⁡ V . is independent of the particle-to-eigenmode phase ) i for for the voltage. R {\displaystyle \beta c} | e ( β ∥ ) ( q L s y x e β {\displaystyle V_{0}=\int E(s)\,\mathrm {d} s} 0 ) ω 1 k ∫ 0 d In symbolic analogy to the longitudinal voltage, one can define effective voltages in two orthogonal directions t If not specified further, the term is likely to refer to the longitudinal effective acceleration voltage d Accelerating Voltage (in KV): Velocity of Electrons: Newtonian: Einsteinian: Difference: Unit: m/sec % Mass of Electrons: kg EU: Energy of Electrons: N*m: Momentum of Electrons: N*sec: Wavelength (deBroglie Equation) of Electrons: m nm: Resolution (Abbe's Equation): m nm Å s V {\displaystyle T(\beta )={\frac {|V_{\parallel }|}{V_{0}}}}, is often defined which relates the effective acceleration voltage ( is a complex quantity. / s s s ⁡ {\displaystyle E_{s}(s,t)=E_{s}(s)\;\exp \left(i\omega t+i\phi \right)}, V → ∥ ( The longitudinal effective acceleration voltage is given by the kinetic energy gain experienced by a particle with velocity $${\displaystyle \beta c}$$ along a defined straight path (path integral of the longitudinal Lorentz forces) divided by its charge, y ∫ ∥ ω − β Note that by the given definition, | The following considerations are generalized for time-dependent fields. In comparison to the former expression, only a phase factor with unit length occurs. x y ~ k β ) In this notation, the effective acceleration voltage , ∥ ω i d → q s Accelerating Voltage in KV 25 SE Electron Emission Coefficient Vs Atomic Number at Various KV Secondary Electron Emission Coefficient 20 Atomic Number 2KV 5KV IOKV 15KV 20KV 80 (b) 25 kV x7,200 x7,200 (a) 30 kV x 2,500 (a) x 2,500 (a) 5kV (b) 25 W x2,200 x 36,000 (b) 25 W x 36.000 . {\displaystyle V_{\parallel }(\beta )=e^{i\phi }\int E_{s}(s)\exp \left(ik_{\beta }s\right)\,\mathrm {d} s}. = ( y c s i {\displaystyle {\tilde {V}}_{x}=|V_{x}|} e ∫ The acceleration voltage is an important quantity for the design of microwave cavities for particle accelerators. β i ⊥ ( ∥ → F ) s ~ β → ω | q ⋅ . 2 ) V ⁡ T]!L�W��O:��>�[�����¡�go�tlU�z�~��3�M�u����Өj�� �䡼G��;�"�dB9�ߐ����9f���e���l�W�j� m�2�0< s → s i = Also, this is an approximation for small-angle deflection of the particle, where the particles trajectory through the field can still be approximated by a straight line. 0 E 1 β . . ⁡ s ∫ ́�(��Ò^��'ꄽ0��&���O*i��ȏ�Čɻ!�9��@��Kf3�H�i��oi����5\���p�x��Y=��N�>"�p������M `*���Y�*�"Op)��_�sI���E�H��B�{�b��0�ŭ�s������. exp must hold. ( V V π β ϕ ) For example, if ( x , are proportional to α ⁡ ) 0 ⋅ ) s s ⁡ β | This is advantageous, since the relative phase between particle and the experienced field was fixed in the previous considerations (the particle travelling through → β {\displaystyle V_{\parallel }(\beta )={\frac {1}{q}}{\vec {e}}_{s}\cdot \int {\vec {F}}_{L}(s)\exp \left(i{\frac {\omega }{\beta c}}s\right)\,\mathrm {d} s={\frac {1}{q}}{\vec {e}}_{s}\cdot \int {\vec {F}}_{L}(s)\exp \left(ik_{\beta }s\right)\,\mathrm {d} s}

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