List of Figures
xi
6.5 Action of a quadrupole or dipole in phase space. . . . . . . . 144
6.6 Mapping of a polygon in phase space. . . . . . . . . . . . . . 145
6.7 An ellipse in phase space. . . . . . . . . . . . . . . . . . . . . 146
6.8 Characteristic points of an ellipse in phase space. . . . . . . . 147
6.9 Sketch of horizontal and vertical β functions of a beamline. . 148
6.10 Transformation of an ellipse under a drift. . . . . . . . . . . . 152
6.11 Plot of the β function in a drift. . . . . . . . . . . . . . . . . 153
7.1 Sketch of an imaging system. . . . . . . . . . . . . . . . . . . 161
7.2 Curvature of the image. . . . . . . . . . . . . . . . . . . . . . 163
7.3 The Browne-Buechner spectrograph. . . . . . . . . . . . . . . 165
7.4 Illustration of the imaging condition arising from Barber’s rule. 166
7.5 Sketch of a generic spectrograph consisting of a single dipole. 168
7.6 Sketch of a generic spectrograph now subject to aberrations up
to order seven. . . . . . . . . . . . . . . . . . . . . . . . . . . 169
7.7 The effect of the aberration (x|aδ). . . . . . . . . . . . . . . . 170
7.8 A magnified drawing of the effect of the aberration (x|aδ). . . 171
7.9 Layout of an example of a fragment separator. . . . . . . . . 175
7.10 Spherical and chromatic aberrations. . . . . . . . . . . . . . . 177
7.11 Cosine-like rays and sine-like rays of the quadruplet corrector. 179
7.12 A quadrupole-octupole C S corrector. . . . . . . . . . . . . . . 179
7.13 A sextupole C S corrector. . . . . . . . . . . . . . . . . . . . . 181
7.14 Sine-like and cosine-like rays of a C S corrected TEM from objective lens to the end of the corrector section. . . . . . . . . 181
7.15 Sine-like and cosine-like rays of the TEAM corrector. . . . . . 182
7.16 Sine-like and cosine-like rays of the TEAM microscope from
objective lens to end of the corrector section. . . . . . . . . . 182
7.17 Spherical and chromatic aberrations of an electron mirror. . . 183
7.18 Geometry of the tetrode mirror in PEEM3. . . . . . . . . . . 184
7.19 Layout of PEEM3. . . . . . . . . . . . . . . . . . . . . . . . . 184
7.20 The beam separator of the first aberration-corrected PEEM. . 185
7.21 The PEEM3 beam separator. . . . . . . . . . . . . . . . . . . 186
7.22 Sine-like, cosine-like and dispersive rays of the PEEM3 beam
separator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
7.23 Aberration-corrected and energy-filtered LEEM at IBM. . . . 187
8.1 Motion in phase space and in the eigenspace when | tr M | > 2. 190
8.2 Relation between the phase space variables and the eigenvectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
8.3 Relation between the eigenvalues when | tr M | < 2. . . . . . . 192
8.4 Motion in phase space and in the eigenspace when | tr M | < 2. 193
8.5 Possible movement of the eigenvalues under small perturbation
near | tr M | = 2. . . . . . . . . . . . . . . . . . . . . . . . . . . 194
8.6 Stable motion in phase space. . . . . . . . . . . . . . . . . . . 197
8.7 Illustration of the case where the beam ellipse and the invariant
ellipses are matched. . . . . . . . . . . . . . . . . . . . . . . . 198
8.8 Behavior of a mismatched beam. . . . . . . . . . . . . . . . . 199
xi
6.5 Action of a quadrupole or dipole in phase space. . . . . . . . 144
6.6 Mapping of a polygon in phase space. . . . . . . . . . . . . . 145
6.7 An ellipse in phase space. . . . . . . . . . . . . . . . . . . . . 146
6.8 Characteristic points of an ellipse in phase space. . . . . . . . 147
6.9 Sketch of horizontal and vertical β functions of a beamline. . 148
6.10 Transformation of an ellipse under a drift. . . . . . . . . . . . 152
6.11 Plot of the β function in a drift. . . . . . . . . . . . . . . . . 153
7.1 Sketch of an imaging system. . . . . . . . . . . . . . . . . . . 161
7.2 Curvature of the image. . . . . . . . . . . . . . . . . . . . . . 163
7.3 The Browne-Buechner spectrograph. . . . . . . . . . . . . . . 165
7.4 Illustration of the imaging condition arising from Barber’s rule. 166
7.5 Sketch of a generic spectrograph consisting of a single dipole. 168
7.6 Sketch of a generic spectrograph now subject to aberrations up
to order seven. . . . . . . . . . . . . . . . . . . . . . . . . . . 169
7.7 The effect of the aberration (x|aδ). . . . . . . . . . . . . . . . 170
7.8 A magnified drawing of the effect of the aberration (x|aδ). . . 171
7.9 Layout of an example of a fragment separator. . . . . . . . . 175
7.10 Spherical and chromatic aberrations. . . . . . . . . . . . . . . 177
7.11 Cosine-like rays and sine-like rays of the quadruplet corrector. 179
7.12 A quadrupole-octupole C S corrector. . . . . . . . . . . . . . . 179
7.13 A sextupole C S corrector. . . . . . . . . . . . . . . . . . . . . 181
7.14 Sine-like and cosine-like rays of a C S corrected TEM from objective lens to the end of the corrector section. . . . . . . . . 181
7.15 Sine-like and cosine-like rays of the TEAM corrector. . . . . . 182
7.16 Sine-like and cosine-like rays of the TEAM microscope from
objective lens to end of the corrector section. . . . . . . . . . 182
7.17 Spherical and chromatic aberrations of an electron mirror. . . 183
7.18 Geometry of the tetrode mirror in PEEM3. . . . . . . . . . . 184
7.19 Layout of PEEM3. . . . . . . . . . . . . . . . . . . . . . . . . 184
7.20 The beam separator of the first aberration-corrected PEEM. . 185
7.21 The PEEM3 beam separator. . . . . . . . . . . . . . . . . . . 186
7.22 Sine-like, cosine-like and dispersive rays of the PEEM3 beam
separator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
7.23 Aberration-corrected and energy-filtered LEEM at IBM. . . . 187
8.1 Motion in phase space and in the eigenspace when | tr M | > 2. 190
8.2 Relation between the phase space variables and the eigenvectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
8.3 Relation between the eigenvalues when | tr M | < 2. . . . . . . 192
8.4 Motion in phase space and in the eigenspace when | tr M | < 2. 193
8.5 Possible movement of the eigenvalues under small perturbation
near | tr M | = 2. . . . . . . . . . . . . . . . . . . . . . . . . . . 194
8.6 Stable motion in phase space. . . . . . . . . . . . . . . . . . . 197
8.7 Illustration of the case where the beam ellipse and the invariant
ellipses are matched. . . . . . . . . . . . . . . . . . . . . . . . 198
8.8 Behavior of a mismatched beam. . . . . . . . . . . . . . . . . 199