Fig. 1. Grouped charges in the drift tube.
The movement of the flow of charges creates an induced current, the direction of which is opposite to the convection, this creates a closed circuit. Thus, if we find the total current flow in Fig.1, we get zero => the law of total current is fulfilled.
Task 5.
5.1 Is it possible to provide high-speed modulation of charged particles in semiconductor devices using the initial part of the field-velocity characteristic?
5.2 Estimate the speed at
which an electron will move in the device, with a characteristic size
of the interaction region of 0.1 microns and a pulse of applied
voltage of 0.1*Ngroup [V]? The material is gallium arsenide. The
pulse duration is Ngroup
s
and Ngroup*
s?
When answering, use the concepts of relaxation times in terms of
momentum and energy.
Given:
d=0.1
U=0.1 V
t1=10-10s
t2=10-14s
Solution:
5.1. It is possible to provide high-speed modulation in semiconductor devices only at a distance of the pulse relaxation length. Charges can be affected by different fields at different points in space. Also, after the relaxation time of the pulse, the charges will dissipate their momentum, changing their direction and giving part of the energy to the scattering center. This process is stabilized through energy relaxation time.
5.2. For calculations, we use the formula for external excitation:
τ
is the relaxation time,
is the velocity under the constant action of excitation on the
electron. Let's define it from the field-speed characteristic (Fig.
2):
Рис.2. Поле-скоростная характеристика
From fig. 2 we can see, that
We will take the relaxation
time
Ответ:
5.2.
Task 6.
6. Determine the amplitude of the "self-consistent" voltage at the grid
gap of the resonator with a
high intrinsic quality, if the amplitude of the first harmonic of the
convection current at the input to the resonator is equal to Nstudent
+2 [mA], the span angle is
,
the accelerating voltage is Ngroup kV, the beam current is 100 mA.
6.1.
Analyze the solution of the problem using the formula:
P(s) J (,v(E))E()dV
Given:
Solution:
The amplitude of the voltage at the grid gap of the resonator:
Let’s calculate the interaction coefficient for a flat gap with a homogeneous field:
Also calculation of the conductivity:
Answer:
Sources: Техника и приборы сверхвысоких частот. Т. II. Электровакуумные приборы СВЧ (Лебедев И.В., Девятков Н.Д. (ред.)) (nehudlit.ru)
6.1 P(s) J (,v(E))E()dV
This formula allows us to calculate the power of the interaction
of the electromagnetic field and the flow of charged particles in the space of their
interaction.
We transform the resulting formula by taking the components of current density, charge; velocities and fields will have constant and variable components.
,
,
,
Therefore, the formula will split into several integrals:
A small angle of flight
indicates an acceleration of the flow (this is taken into account in
the solution,
>0)
, which means:
Considering the interaction of a constant flow and an alternating field (or vice versa), we come to the conclusion: for a period, this value will be equal to 0.
However, it is this interaction that leads to the modulation of velocity (and later to the modulation of density). This fact is also used in the solution.
Considering the interaction of a modulated flow with an alternating field, we average the convection current and the induced current. Knowing the induced current (from the problem condition), we will make the transition to the desired power.
Thus, the original solution is correct and corresponds to all the provisions mentioned above. The self-consistent voltage in the first case is sought by introducing an equivalent electronic conductivity, taking into account all the above facts. When substituting the received data into a given formula, a power value corresponding to a resonator with a high Q-factor value will be obtained. Roughly estimate the efficiency of the resonator:
