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'''Electron optics''' is a mathematical framework for the calculation of particle paths along given [[electrostatic]] or [[magnetostatic field]]s. The term ''optics'' is used because a [[charged particle beam]] can be manipulated using [[magnetic lens]]es in a similar fashion to the manipulation of a light beam with [[optical lens]]es.
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Electron optics calculations are, besides other uses, needed for [[electron microscopes]] and are also crucial for the design of modern [[particle accelerators]]. In [[paraxial approximation]], the calculations can be done using [[ray transfer matrix analysis]].
 
== Electron properties ==
{{main|Electron}}
Electrons are charged particles ([[point charge]]s with [[rest mass]]). The electron also has an associated [[spin (physics)|spin]] of + 1/2. While in motion an electron possesses [[kinetic energy]], regardless of any imposed charge field—this could be achieved by accelerating electrons via a voltage differential into a screened "field-free" region, which initially imparts the energy required to accelerate the electron. Given sufficient voltage, the electron can be accelerated sufficiently fast to exhibit measurable [[relativistic effect]]s, and the velocity must be accounted for relativistically. According to the [[wave particle duality]], electrons can also be considered as wave propagations and therefore have associated wave properties such as wavelength, phase and amplitude.
 
With respect to electron optics, the nature of the electron as a charged particle causes electrons to interact with imposed electron fields, and their spin causes magnetic field interactions as well. These interactions form the fundamentals of electron optical theory.
 
== Field interactions ==
 
=== Particle interpretation ===
Magnetic fields interact with an electron in a manner that alters velocity independently of kinetic energy (velocity magnitude). Electrons move according to the [[cross product]] of the magnetic field and the electron propagation vector, such that, in an infinite uniform field moving electrons take a [[circular motion]] at a constant radius dependent upon electron velocity and [[magnetic field strength|field strength]] according to the following equation, which can be derived from circular motion:
 
:<math> r =  \frac{2 m cv}{eH}</math>
 
where ''r'' is the orbit radius, ''m'' is the mass of an electron, ''v'' is the electron velocity, ''e'' is the charge on the electron and ''H'' is the applied magnetic field. Electrons that have a velocity component that is parallel to the magnetic field will rather "stretch out" the circle and form [[helix|helical]] paths, the pitch of which is subject to the rotation period and the parallel velocity component.
 
In the case of an applied electrostatic field, an electron will deflect towards the positive gradient of the field. Notably, this crossing of electrostatic field lines means that electrons, as they move through electrostatic fields change the magnitude of their velocity, whereas in magnetic fields, only the velocity direction is modified.
 
As electrons can exhibit non-particle (wave-like) effects such as [[diffraction]], a full analysis of electron paths can be obtained by solving [[Maxwell's equation]]—however in many situations, the particle interpretation may provide a sufficient approximation with great reduction in complexity.
 
One further property of electrons is that they interact strongly with matter as they are sensitive to not only the nucleus, but also the matter's electron charge cloud. Therefore electrons require [[vacuum]] to propagate any reasonable distance, such as would be desirable in electron optic systems. Penetration in vacuum is dictated by [[mean free path]], a measure of the probability of collision between electrons and matter, approximate values for which can be derived from [[Poisson statistics]].
 
=== Quantum theory ===
Although not very common, it is also possible to derive effects of magnetic structures to charged particles starting from the [[Dirac equation]].<ref>{{Cite doi | 10.1016/0375-9601(89)90685-3 }}</ref>
 
== See also ==
* [[Charged particle beam]]
* [[Strong focusing]]
* [[Electron beam technology]]
* [[Electron microscope]]
* [[Beam emittance]]
* [[Ernst Ruska]]
 
== References ==
{{reflist}}
{{refbegin}}
*:[http://www.ml.afrl.af.mil/facilities/mll-cmc-eo.html Air Force Research Laboratory - Electron Optics Program]
{{refend}}
 
{{DEFAULTSORT:Electron Optics}}
[[Category:Electromagnetism]]
[[Category:Accelerator physics]]

Latest revision as of 05:01, 10 December 2014

is a combined development in Balestier with 104 residential apartment units from the 5th to 18th storey, four industrial store items on the first & 2nd storey and 6 office items on the third & 4th storey.

Jointly developed by Keppel Land Limited and China Vanke Co Ltd, the condominium is simply a stone's throw away from the Tanah Merah MRT station and surrounded by schooling institutes such as Anglican Excessive Faculty, Temasek Junior College and the up and coming SUTD (Singapore College of Know-how and Design) new campus which is predicted to be ready by 2014. Upcoming new launch alongside Fernvale Close and Seng Kang West Approach in District 19, this will be a brand new mission by UOL Group Limited. We're accumulating interest for VVIP preview TO SENTOSA. TO SUPERMARKETS. TO CINEMAS. TO RESORTS WORLD SENTOSA. TO RAFFLES PLACE. TO SHENTON METHOD. TO COMMON STUDIOS. TO CHINATOWN. TO SINGAPORE BASIC HOSPITAL. TO AYE. TO SCHOOLS. TO MARINA AT KEPPEL BAY. TO MALLS.

An opulent and modern way of life awaits you at Inflora condo which is a brand new launch Pasir Ris that encompasses amazing facilities / services and amazing hot spots of Singapore. Inflora Condominium is constructed near to the upcoming Tampines East MRT station which is only strolling distance away, making this flora street condo much more precious. This Pasir Ris apartment consists of facilities equivalent to, waterjet pool, swimming pool, club home, dining pavilion and many extra. Simply at Inflora condo alone, you and your family members can take pleasure in fun-stuffed day all the way to the night time.

Upcoming Singapore new property launch But when you dropped in here by mistake once you're actually in search of property to buy, please see Singapore Property Gross sales for new property launches in Singapore.) What are new property launches in Singapore about? NEW LAUNCH How you can get reductions at new property launches in Singapore Singapore new condo launch you can trust! News on new launches of Singapore residences New Launch Singapore Property Condo Apartment Landed Private Property Industrial Shop Office Industrial Resale Subsale Rental This information to property launches in Singapore explains terminology & processes involved in buying property in Singapore at such launches. Click links below for answers. Information Bites on Singapore New Property Sales 2012 Just Launch Apartment

Goodies given away on the sales gallery are a catalyst to close deals. Be it price absorption, furnishings vouchers, furnishing packages, or branded home equipment, they are attractive concessions in the eyes of potential buyers. Never thoughts the truth that such offers are simply peanuts in contrast with the price of the property. Furthermore, spectacular views out of your very personal unit aren't the only issues that comes free with every make investments. Amenities made obtainable for residents are accessible all-year long. Lap pools, youngsters playground, and a parking lot for each unit every property provision and can be utilized freely. Wanting first hand data for above upcoming Undertaking go away your contact CLICK ON RIGHT HERE New Condominium 2014 in February NEW Condominium Inflora @ flora drive Fully Offered

This widespread lease choice will be based mostly on any number of elements. While market issues at all times play in for property traders, the standard homeowner could also be more concerned with monetary comfort and passing on their Singapore property to the following era. Commonwealth Towers is the upcoming new launch which is situated just minutes away from the Queenstown MRT comprising a complete of 845units! Project is inside District 03 close to to Singapore Orchard Street New launch apartment in Singapore will give you extra possibility other then resale market, when there's something on the market that excites you, consider in your self, consider in us, Why submit cheques to register for new property launches in Singapore? New Launch at District 14 Personal Condominium

The close by private housing developments are mainly low-rise landed property giving more privateness and exclusivity to the brand new improvement. The virtually unspoil surroundings is what differentiates this development from the encircling ones (VII) Park Connector There were students, retirees and property brokers napping, snacking and taking part in cards within the queue to kill time. Such a scene made passers-by wonder if the gang actually consisted of real patrons, or simply half-timers being paid to faux how scorching the brand new undertaking was. With the steam of an overheated property market dying down, the buzz has now shifted to developers enjoying discount video games to push new initiatives or clear outdated stock. With so many ‘nice offers', buyers are spoiled for decisions.

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