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An Introduction to Beam Physics
tube was until recently the most important application of particle optics. In
this case, for each color an electron beam is deflected vertically and horizontally by two simple magnetic deflectors in order to sweep over the screen area,
and the intensity of each beam is adjusted according to the color saturation
at the respective point. The cathode ray tubes used in the oscilloscopes use
electrostatic deflection plates to achieve high frequency. Yet the limit of a single pair of plates is around 150 MHz, above which the single pair is replaced
with segmented pairs of plates. This type of deflector can reach a frequency of
300 MHz. To reach even higher frequency, a double helix line is used to deflect
the beam, which has reached 10 to 20 GHz. Nowadays, 33 GHz oscilloscopes
are commercially available.
At any given point on the screen, the resulting spot should not be wider
than the distance between two pixels, so whatever size the beam had initially
should not be amplified very much; so
(x|x) and (y|y)
should not be large.
The requirements for aberrations are usually benign as the phase space
volume of the beam is small. Yet those aberrations do limit performance and
over the decades various ways have been developed to minimize them. The
advent of plasma and liquid crystal displays (LCD) for TV on one hand and
digital oscilloscopes on the other has caused a precipitous decline of the use
of cathode ray tubes, which are preferred now only in specialized markets.
7.2 The Camera and the Microscope
The purpose of a camera and an electron microscope is to create an
image of an object formed by light or particle rays. The quantities
(x|x) and (y|y)
are magnifications, and in most cases it is desirable to have them equal.
The electron microscope is just a special case in which both of them are made
to be very large to increase the resolution.
If a true image is desired, it is important that the relationship between
final and initial coordinates is really linear, which requires that all higher
order position dependent matrix elements vanish, and so
(x|xx) = 0, (y|yy) = 0, (x|xxx) = 0, . . . .
In reality, of course, it is difficult to achieve this to higher orders, hence
some distortion remains. In the case of an electron microscope, this is often
An Introduction to Beam Physics
tube was until recently the most important application of particle optics. In
this case, for each color an electron beam is deflected vertically and horizontally by two simple magnetic deflectors in order to sweep over the screen area,
and the intensity of each beam is adjusted according to the color saturation
at the respective point. The cathode ray tubes used in the oscilloscopes use
electrostatic deflection plates to achieve high frequency. Yet the limit of a single pair of plates is around 150 MHz, above which the single pair is replaced
with segmented pairs of plates. This type of deflector can reach a frequency of
300 MHz. To reach even higher frequency, a double helix line is used to deflect
the beam, which has reached 10 to 20 GHz. Nowadays, 33 GHz oscilloscopes
are commercially available.
At any given point on the screen, the resulting spot should not be wider
than the distance between two pixels, so whatever size the beam had initially
should not be amplified very much; so
(x|x) and (y|y)
should not be large.
The requirements for aberrations are usually benign as the phase space
volume of the beam is small. Yet those aberrations do limit performance and
over the decades various ways have been developed to minimize them. The
advent of plasma and liquid crystal displays (LCD) for TV on one hand and
digital oscilloscopes on the other has caused a precipitous decline of the use
of cathode ray tubes, which are preferred now only in specialized markets.
7.2 The Camera and the Microscope
The purpose of a camera and an electron microscope is to create an
image of an object formed by light or particle rays. The quantities
(x|x) and (y|y)
are magnifications, and in most cases it is desirable to have them equal.
The electron microscope is just a special case in which both of them are made
to be very large to increase the resolution.
If a true image is desired, it is important that the relationship between
final and initial coordinates is really linear, which requires that all higher
order position dependent matrix elements vanish, and so
(x|xx) = 0, (y|yy) = 0, (x|xxx) = 0, . . . .
In reality, of course, it is difficult to achieve this to higher orders, hence
some distortion remains. In the case of an electron microscope, this is often