This document summarizes information about magnetrons, which are microwave devices that use magnetic and electric fields to generate microwaves. Some key points:
1) Magnetrons were an early microwave device and were crucial for radar technology in World War II, allowing for the development of high-power microwave sources. Commercial magnetrons now provide powers up to several megawatts.
2) Magnetrons operate by using magnetic and electric fields to cause electrons emitted from a cathode to travel in spiral paths around an anode, interacting with resonant cavities to generate microwave oscillations.
3) The electrons form a cloud-like structure called the Brillouin cloud, confined by the magnetic field. The Hull cutoff condition relates the
Radars are very complex electronic and electromagnetic systems. Often they are
complex mechanical systems as well. Radar systems are composed of many different
subsystems, which themselves are composed of many different components. There is a great
diversity in the design of radar systems based on purpose, but the fundamental operation and
main set of subsystems is the same.
RADAR - RAdio Detection And Ranging
This is the Part 2 of 2 of RADAR Introduction.
For comments please contact me at solo.hermelin@gmail.com.
For more presentation on different subjects visit my website at http://www.solohermelin.com.
Part of the Figures were not properly downloaded. I recommend viewing the presentation on my website under RADAR Folder.
The following presentation deals with some basic introduction of the role that electronics play in defence..... The article is quite intresting and tried to kept in most easy and eyecatching way as possible.
microprocessor based automatic synchroniser (8085)BIJU GANESH
It is well known that electrical load on a power system or an
industrial establishment, is never constant but it varies. To meet the requirement of
variable load , economically and also for assuring continuity of supply the number of
generating units connected to a system busbar are varied suitably . The connection of
an incoming alternator to system bus, ie; synchronization requires fulfillment of the
condition like the same phase sequence equality of voltages and frequency between
the incoming machine and frequency between the in coming machine and busbar.
Radars are very complex electronic and electromagnetic systems. Often they are
complex mechanical systems as well. Radar systems are composed of many different
subsystems, which themselves are composed of many different components. There is a great
diversity in the design of radar systems based on purpose, but the fundamental operation and
main set of subsystems is the same.
RADAR - RAdio Detection And Ranging
This is the Part 2 of 2 of RADAR Introduction.
For comments please contact me at solo.hermelin@gmail.com.
For more presentation on different subjects visit my website at http://www.solohermelin.com.
Part of the Figures were not properly downloaded. I recommend viewing the presentation on my website under RADAR Folder.
The following presentation deals with some basic introduction of the role that electronics play in defence..... The article is quite intresting and tried to kept in most easy and eyecatching way as possible.
microprocessor based automatic synchroniser (8085)BIJU GANESH
It is well known that electrical load on a power system or an
industrial establishment, is never constant but it varies. To meet the requirement of
variable load , economically and also for assuring continuity of supply the number of
generating units connected to a system busbar are varied suitably . The connection of
an incoming alternator to system bus, ie; synchronization requires fulfillment of the
condition like the same phase sequence equality of voltages and frequency between
the incoming machine and frequency between the in coming machine and busbar.
Describes Fiber Optics using Optical Ray Theory.
For comments please contact me at solo.hermelin@gmail.com.
For more presentations visit my website at http://www.solohermelin.com.
Power Theft Identification and Monitoring using GSM moduleAshishPanchdhar1
developed the system were we are using Arduino Atmega328 and current sensors and GSM module attached to every pole. The current sensor keeps the track of amount of current pass through it. When this supply reaches to other end of the pole than the current sensor available at pole 2 will measure the current receive and gives the reading to the Arduino Atmega328. Then the Arduino compares the current readings to the previous readings and if the supply is not approximately equal than the Atmega328 trigger the GSM module. Then the GSM module will send the SMS to the distributor that the amount of current received is not approximately equal and there is some illegal action occurred in the section from pole 1 to pole 2. This will help the distributor to overcome the losses and where the losses will be take place and the theft of the electricity
Describes Fiber Optics using Optical Ray Theory.
For comments please contact me at solo.hermelin@gmail.com.
For more presentations visit my website at http://www.solohermelin.com.
Power Theft Identification and Monitoring using GSM moduleAshishPanchdhar1
developed the system were we are using Arduino Atmega328 and current sensors and GSM module attached to every pole. The current sensor keeps the track of amount of current pass through it. When this supply reaches to other end of the pole than the current sensor available at pole 2 will measure the current receive and gives the reading to the Arduino Atmega328. Then the Arduino compares the current readings to the previous readings and if the supply is not approximately equal than the Atmega328 trigger the GSM module. Then the GSM module will send the SMS to the distributor that the amount of current received is not approximately equal and there is some illegal action occurred in the section from pole 1 to pole 2. This will help the distributor to overcome the losses and where the losses will be take place and the theft of the electricity
Hanna skliarova porosity of nb magnetron sputtered thin films and dependenc...thinfilmsworkshop
Pinholes (or through film porosity) in Nb thin film deposited on the inner walls of SRF cavities are harmful for cavity performance because they may expose inferior copper that has much higher resistance than niobium at 4.2 K. Aluminated quartz substrates allowed us to make visible the pore sites for inspection and counting by production visible corrosion products. We showed the correlation between the amount of pinholes in niobium thin film prepared by magnetron sputtering and the deposition parameters, such as sputtering gas pressure, substrate temperature, applied bias, placing of the sample in UBM sputtering mode. Thus low temperature of the substrate and high sputtering gas pressure promoted growth of a voided film (that corresponds to SZM approach) with high amount of pinholes. Heating of the substrate during deposition has resulted in moderate decrease of the pinhole amount, while negative bias applied to the substrate showed stronger decrease of the pinhole amount thanks to additional bombardment of the substrate by Ar+ serving to remove weakly bounded particles during deposition.
Daniel adrien franco lespinasse - status of magnetron sputtered qwrthinfilmsworkshop
The objective of this research is the deposition of a superconductive thin film onto copper Quarter Wave Resonator cavities that can be used in the HIE-ISOLDE facility at CERN. To do this, it was developed an innovative magnetron configuration source. Our experience has shown the efficiency of this particular configuration in order to deposit a uniform thin film, and also improve the superconductive properties of the niobium (Residual Resistance Ratio and Critical Temperature). This presentation presents the recent improvement of the niobium thin film properties and the procedure used to deposit and measure the first resonator at LNL of HIE-ISOLDE type.
http://www.surfacetreatments.it/thinfilms
Cylindrical Post-Magnetron sputtering for High Rate Niobium deposition (Cristian Pira - 15')
Speaker: Cristian Pira - INFN-LNL | Duration: 15 min.
Abstract
The use of Nb/Cu cavity at CERN for the LEP and at the INFN-LNL for Alpi Linac has demonstrated the possibility to use this technology for particles accelerators to substitute the more expensive technology of niobium bulk cavity. The limit of the Nb/Cu cavity is the Q-slope, which decreases the Q factor at high accelerating fields. The accelerators community supposes that it’s possible to eliminate, or to decrease, the problem of Q-slope with high pure films of sputtered niobium. One way to obtain pure films is to decrease the number of impurities enclosed in the growing film.
It’s possible to reduce the number of impurities when the sputtering rate process increases.
We study the possibility to enhance the plasma density in order to increase the sputtering rate and then reduce the impurities in the niobium sputtered film and finally obtain high pure films.
In order to enhance the plasma density we sputter the niobium target with high currents to heat it and get to thermoionic emission. This sputtering method is called high rate sputtering.
First results of Niobium coatings will be presented.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
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In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
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This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
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Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
2. Magnetrons
• Early microwave device
– Concept invented by Hull in 1913
– Initial devices in 1920’s and 30’s
• Cavity Magnetron (UK) – 10 kW
– Rapid engineering and Production
– Radiation Lab (MIT) established
• Relativistic Cavity Magnetron (1975) –
900MW
• Advanced Relativistic Magnetrons (1986) -
8 GW
• Commercial Magnetrons (2003) - 5 MW
3. Magnetrons
• Inherently efficient
• Delivers large powers (up to GW pulsed
power and MW cw)
• Limited electronic tuning, i.e., BW limited
• Low cost
• Industrial uses
– microwave ovens
– industrial heating
– drying wood
– processing and bonding materials
4. Magnetrons
• B no longer used to confine electron beam
as in a Klystron - B is an integral part of rf
interation.
• Multicavity block
• Coaxial cathode
• Coupling - I/O- loop or Waveguide
7. Planar Magnetron
Let VA = potential difference
between the anode and
cathode, and E0=- VA /d. An
x z applied magnetic field is in
the x direction (into the
paper). The force on the
electrons becomes:
F = m dv/dt = e[E 0 + v × B0 ], E 0 → y, B0 → x
ˆ ˆ
d 2x dx
2
=0⇒ = v x 0 = assume to be zero (initially)
dt dt
d2y e dz e dz
2
= [E 0 − B0 ] = E 0 − ωc
dt m dt m dt
d 2z e dy dy eB
2
= [ B0 ] = ωc ; where ωc ≡
dt m dt dt m
8. Planar Magnetron
dy dz dp dq e
Let q ≡ &p≡ ∴ = ωc q & = E 0 − ωc p
dt dt dt dt m
d2p
+ ωc p = ωc (E 0 / B0 )
2 2
dt 2
∴ p = M cos ωc t + N sin ωc t + (E 0 / B0 )
dp
= ωc q = −ωc M sin ωc t + ωc N cos ωc t
dt
q = − M sin ωc t + N cos ωc t
at t = 0, p = v z0 and q = v y0 ∴ M = v z0 - (E 0 / B0 ); N = v y0
dy
∴ = v y0 cos ωc t + [(E 0 / B0 ) − v z0 ] sin ωc t
dt
dz
= v y0 sin ωc t + [(E 0 / B0 ) − v z0 ][1 − cos ωc t ] + v z0
dt
9. Planar Magnetron
∴ y( t ) = ( v y 0 / ωc ) sin ωc t + (1 / ωc )(−E 0 / B0 + v z 0 )(cos ωc t − 1)
sin ωc t E 0
z( t ) = ( v y 0 / ωc )(1 − cos ωc t ) + ( v z 0 − E 0 / B0 ) + (t)
ωc B0
10. Planar Magnetron
If v z 0 = 0 and v y 0 = v 0 , then this result can be written as
2 2 2 2
E0 E0 v0 E0
z −
(t) + y −
= +
ω ω B
B0 ωc B 0 c c 0
This neglects space charge - tends to
make trajectory more “straight”.
Result - frequency of cycloidal motion
is ωc ∴ f ∝ B and (e/m)
KEY: average drift velocity of electrons in z direction is E0/B0 ,
independent of vz0 and vy0.
11. uox here is the
v0z of our
formulation
ref: Gerwartowski
12. Planar Magnetron
Electrons have dc motion equal to E0/B0, slow wave structure is
assumed to be a propagating wave in the direction of the
electron flow with a phase velocity equal to E0/B0
15. Circular Magnetron
(conventional geometry)
Electrons tend to
move parallel to
the cathode. After
a few periods in
the cylindrical
geometry the
electron cloud so
formed is known
as the Brillouin
cloud. A ring
forms around the
cathode.
17. Brillouin Cloud
Next, compute the electron
angular velocity dθ/dt for
actual geometry. Note
region I inside the Brillouin
cloud and region II outside.
Equations of motion
2
d 2 r dθ e dθ d 2z
2
− r = − E r + Bz r , (1); 2 = 0
dt dt m dt dt
1 d 2 dθ e dr
r = Bz , (2); by eqn (2)
r dt dt m dt
d 2 dθ dr d ωc 2 2 dθ ωc 2
r = ωc r = r ∴ r = r + constant
dt dt dt dt 2 dt 2
18. Brillouin Cloud
dθ ω 2
At r = rc ,
= 0 ∴ constant = - c rc
dt 2
dθ ωc rc
2
∴ = 1 − 2
dt 2 r
Note: electrons at the outermost radius of the cloud (r = r0)
move faster than those for r < r0. The kinetic energy (of the
electrons) increase is due to drop in potential energy.
m 2 m dr dθ
2 2
1 dθ dr
mv = eV or V = v = + r Assume that r
2
>>
2 2e 2e dt dt
dt dt
2
( ) r − rc
2 2 2
m ω 2 eB 2
eB
2
∴ V = r 2 c 1 − rc / r 2 = 0 , where ωc ≡
2e 4 8m r m
19. Hull Cutoff Condition
For a given B0, the maximum potential difference VA that can be
applied between the anode and cathode, for which the Brillouin
cloud will fill the space to r = ra is
2
ra − rc
eB0
2 2 2
VA max = or for a given VA ∃ a minimum
r
8m
a
B required to avoid filling the anode - cathode gap :
2
8m ra
VA 2 , the Hull cutoff condition
2
B0min = r −r 2
e a c
20. Hull Cutoff Condition
B0 < B0min direct current flows to anode
and no chance for interaction with rf.
B0 > B0min Brillouin cloud has an outer
radius r0 < ra and no direct current
flows to the anode. For a typical
magnetron, B0 > B0min therefore r0 < ra
ra
B0min = 45.5 VA 2 2
, the Hull cutoff condition where
ra − rc
VA is in volts, r in cm and B in Gauss. In designing a magnetron,
2
eB0
2
r0 − rc
2 2
generally, V(r = r0 ) = ≈ (0.1 to 0.2) VA
8m r
0
21. Magnetron Fields
From radial force equation (1), consider electrons following
circular trajectory in Brillouin cloud. Assume that
d 2r
2
is small, and solve for E r in region I, (r < r0 ) :
dt
rθ 2
rθ
ErI =
− rθB0 = dθ
(θ − ωc ), insert the result for θ =
e/m e/m dt
r ωc r 2 − rc 1 rc
2 2 2
ErI = 1 − 2 − 1
2 r
2
e/m 2 r
r m (eB0 ) 2 rc 1 rc
2 2
ErI = − 2 1 − 1 +
2 e m r 2 r
e ( B0 ) 2 rc 4
ErI = − r 1 −
m 4 r
22. Magnetron Fields
From Poisson’s equation the charge density:
ε0 ∂
ρ 0 = ε 0∇ ⋅ E = (rE r I )
r ∂r
∂ ∂ 2 rc
4
e ( B0 ) 2
(rE r I ) = κr (1 − ), where κ ≡ −
∂r ∂r
r m 4
rc
4
rc 4 rc 4 rc 4
= κ 2r (1 − ) + r 2 4 5 = 2rκ 1 − + 2
r
r r
r
rc 4 e ( B0 ) 2 rc 4
ρ 0 = 2ε 0κ 1 + = − ε 0 1 +
r
m 2 r
ρ0 falls slightly as r increases from rc (can increase ρ0 by increasing
ρ
B0 which follows as electrons spiral in smaller cycloidal orbits 0
about the cathode.
23. Magnetron Fields
Outside the Brillouin cloud, r0 < r < ra, in region II, use Gauss’s
Theorem:
r0
∫ D ⋅ ds = ε E
surface
0 r II 2πrdz = Q encl = ∫ ρ0 (r )2πr dr dz
rc
r0 4 2 2 4 4
rc r0 rc 1 rc 1 rc
= κ1 ∫ (r + 3 )dr = κ1[ − − 2
+ 2
]
rc
r 2 2 2 r0 2 rc
2 4
r0 rc 2πe(B0 ) 2 ε 0
= κ1[ − 2 ], where κ1 ≡ dz
2 2r0 2m
4 4 4
2 rc e(B0 ) 2 1 r0 − rc
∴ ε 0 E r II 2πrdz = [r0 − 2 ] or E r II = − [ 2
]
2r0 4m r r0
24. Hartree Relationship
The potential difference VA between the cathode and anode to
maintain the Brillouin cloud of outer radius r0 is given by:
ra r0 ra
VA = − ∫ E r dr = − ∫ E rI dr − ∫ E rIIdr
rc rc r0
2 r0 4 2 ra 4 4
e( B 0 ) rc e( B 0 ) 1 r0 − rc
=
4m ∫ r(1 − r 4 )dr + 4m
rc
∫ r [ r0 2 ]dr
r0
r 2 1 r 4 r0 r 4 − r 4
e( B 0 ) 2
ra
= + c2 + ( 0 2 c ) ln r
4m 2 2 r r r0 r0
c
=
e(B0 ) r0 − rc
2
2 2
( ) 2
+ 2(
4
r0 − rc
4
ra
) ln( ), Hartree Relationship
8m r0 2 r0
2
r0
25. Hartree Relationship
VA =
2
e( B 0 ) 0
(
r 2 −r 2 2
c ) + 2(
4
r0 − rc
4
ra
) ln( )
2 2
8m r0 r0 r0
or the Hartree Relationship maybe expressed by
ra VA − VB
ln( ) = 4 4
, where is VB is voltage at r = r0
r0 ωc B0 r0 − rc
( 2
)
4 r0
2 2
ω r − rc ) = circular velocity at r = r
v B = r0 θ = c ( 0 0
2 r0
This vB is important since it gives the velocity of the electrons at the
outer radius of the Brillouin cloud. It is this velocity vB that is to
match the velocity of the traveling waves on the multicavity structure.
26. Anode - Cathode Spacing
Again, consider the planar version of the magnetron;
r0 − rc is small fraction of ra − rc such that
VB (r = r0 ) ≈ (0.1 to 0.2) VA
Desire microwave field repetition with spatial periodicity of the
structure. This field will have traveling wave components the most
important of which is a component traveling in the same direction
with
27. Anode - Cathode Spacing
These traveling waves are slow waves with the desired phase velocity,
vp ~ vB. Consider the wave equation as follows:
∂ 2E ∂ 2E ∂ 2E
∇2E + k 2E = 2 + 2 + 2 + k 2E = 0
∂x ∂y ∂z
Fields traveling in z direction e j( ωt -βz) , β = ω/v p , ∂/∂x = 0
∂ 2E ∂ 2E
∴ 2 − (β 2 − k 2 )E ≈ − β 2 E = 0, since
∂y ∂y 2
ω2 ω2
k 2 = 2 << β 2 = 2
c vp
since v p ~ v B , electron velocity << c
28. Anode - Cathode Spacing
The solution of this equation results in hyperbolic trig functions:
ω ω
A sinh y z + B cosh
ˆ y yˆ
v v
∴E = p p e j( ωt -βz) , d ≡ r − r
a c
ω
sinh d
v
p
ωd/vp → not too large, such that the E at Brillouin layer is
insufficient for interaction
ωd/vp → not too small such that the E is so large that fields exert
large force on electrons and cause rapid loss to the anode thereby
reducing efficiency. Typically,
(ωd ) / v p = (ω / v p )(ra − rc ) ≈ 4 to 8
29. Multicavity Circuit - Slow Wave Structure
Equivalent circuit of multicavity
structure - here each cavity has been
replaced by its LC equivalent. This
circuit is like a transmission line
filter “T” equivalent.
j ωL 1
Z1 = , ω0 = Z1 = impedance of
1 − ( ω / ω0 ) 2
LC
parallel LC network representing the uncoupled cavity
1
Z2 = C c = coupling capacitance between
j ωC c
2πε0
cavity vane and cathode = ⇒ from coaxial line
ln(ra / rc )
30. Multicavity Circuit - Slow Wave Structure
The circuit acts like low-loss filter
interactive impedance = input
impedance of an infinite series of
identical networks.
Z1 [( Z1 / 2) + Z k ]Z 2
Zin = + = Z k , solve for Z k to find
2 Z 2 + ( Z1 / 2) + Z k
2
Z k = [( Z1 / 4) + Z1Z 2 ]1/2 If Zin = Z k is pure resistive, the generator " sees"
resistance load and delivers power. Otherwise no power is delivered.
2 2
If Z1 = ± jX a ; Z 2 = jX b then Z k = [(−X a / 4) + X a X b ]1/2 ∴ X a X b > X a / 4
to be real or X b > X a / 4 or Z 2 > Z1 / 4, Z k = Z1Z 2 1 + Z1 /( 4 Z 2 ) ,
- 1 < Z1 /(4 Z 2 ) < 0 is the pass band. Phase shift per section θ = βp of filter is
θ = β p = 2 sin -1 − Z1 /( 4 Z 2 ) = 2 sin -1 ω2 LCc /{4[1 − (ω / ω0 ) 2 ]}
31. Multicavity Circuit - Slow Wave Structure
Rf field repeats with periodicity p
(spacing of adjacent cavities). Field at
distance z+np is same as z. β = phase
shift per unit length of phase constant of
wave propagating down the structure.
For a circular reentrant structure anode with N cavities, fields
are
indistinguishable for Z as for Z + np. 2πm πm
βNp = 2πm m = 0, 1, 2, ... N/2 for N = 6, βp = = , m = 0,1,2,3
6 3
for m = N/2, βp = π or π mode (per cavity)
∴θ = βp = π = 2 sin -1 ω 2 LCc /{4[1 − (ω / ω0 ) 2 ]} or
π ω 2 LCc ω0
sin = 1 = solve for ω. ω = ωπ = is the
2 4[1 − (ω / ω0 ) ]
2
1 + Cc /(4C )
operating frequency for the π mode.
32. Fields and Charge Distributions for two
Principal Modes of an Eight-Oscillator
Magnetron
33. Fields and Charge Distributions for two
Principal Modes of an Eight-Oscillator
Magnetron
34.
35. Multicavity Circuit - Slow Wave Structure
For the m = N/2 - 1 mode
ω(N/2)-1 π 2 1 Cc
≈ 1− ≈ 0.97 to 0.99
ωπ 4 N C
∴ Competing modes - desire to increase this separation
2 methods - strapping and rising sun. Strapping adds
capacitance ∴ lowers the frequency of the π mode :
ω0 ωπ ωπ
ωπ = vp = = r0 , β 2πr0 = Nπ
1 + Cs / C + Cc /(4C ) β N /2
38. Typical Magnetron Cross-Sections (after Collins)
(d) Single ring strap connecting alternate vanes
(e) Rising sun anode with alternate resonators
of different shapes
(f) Inverted magnetron with the cathode exterior
to the anode
39.
40.
41. The unfavorable electrons hit the cathode and give up as heat excess
energy picked up from the field. As a result, the cathode heater can
be lowered or even turned off as appropriate.
two
two
42. Rotating wheel formed by the favorable electrons in
a magnetron oscillating in the π mode ref: Ghandi
43.
44. General Design Procedures for Multicavity
Magnetrons
V,I requirements: From Power required may select VA.
High VA → keeps current down and strain on cathode, but
pulsed high voltage supplies are needed.
Note Pin = P0 / efficiency and I A = Pin / VA= P0 / ηVA.
Cathode radius from available current densities for type of cathodes
typically used in magnetrons.
Typically J0 (A/cm2) → 0.1 to 1.0 for continuous, 1 to 10 for pulsed
Smaller J0 → lower cathode temperature so longer life of tube
Too low J0 → requires a larger rc
45. General Design Procedures for Multicavity
Magnetrons
Emitting length of cathode (lc) < anode length, la ; Typically,
lc ~ 0.7 to 0.9 la , and la < λ/2 (prevents higher order modes)
Smaller la is consistent with power needs less B0 needed (less weight)
Radius r0 (top of Brillouin cloud) from velocity synchronism
condition:
vp (r = r0) = ωπ r0 / (N/2) = [ωc r0 /2] [1- (rc2 / r02)]; therefore
r0 = rc / [1-(ωπ /ωc)(4/N)]1/2
For an assumed B0, r0 can be calculated for a number of values of N
(typically 6 to 16) or 20 to 30 for a small magnetron.
46. General Design Procedures for Multicavity
Magnetrons
Voltage eVB (r = r0) = (1/2) mvB2 where vB = vp (r = r0) or
VB = (vB /5.93x107) 2 ; vB in cm/sec ; Hence VB ~ 0.1 to 0.2 VA
Note efficiency, η < (1 - VB / VA )*100; hence
Smaller VB / VA contributes to improved efficiency
Anode radius: ln (ra/ r0) = [VA - VB ] / {[ωc 2 / 4(e/m)][(r0 4 -rc 4 ) / r0 2 ]}
Also Bmin = (45.5 VA) 1/2 [ra /(ra 2 -rc 2 )] << B0
(ω /vp)( ra - rc) ~ 4 to 8
N must be even such that Nπ phase shift around the circumference is a
whole 2 π.