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Achieving temporary divertor plasma detachment with MARFE events by pellet injection in the EAST superconducting tokamak
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2017 Plasma Sci. Technol. 19 015101
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Achieving temporary divertor plasma detachment with MARFE events by pellet injection in the EAST superconducting tokamak
Guozhong DENG(邓国忠)1,2,Liang WANG(王亮)1,Xiaoju LIU(刘晓菊)1,
Yanmin DUAN(段艳敏)1,Jiansheng HU(胡建生)1,Changzheng LI(李长征)1,
Ling ZHANG(张凌)1,Shaocheng LIU(刘少承)1,Huiqian WANG(汪惠乾)1,
Liang CHEN(陈良)1,Jichan XU(许吉禅)1,Wei FENG(冯威)1,
Jianbin LIU(刘建斌)1,Huan LIU(刘欢)1,Guosheng XU(徐国盛)1,
Houyang GUO(郭后扬)1,Xiang GAO(高翔)1,2and the EAST team
1Institute of Plasma Physics,Chinese Academy of Sciences,Hefei230031,People’s Republic of China
2University of Science and Technology of China,Hefei230026,People’s Republic of China
E-mail:xgao@https://www.doczj.com/doc/aa9778990.html,
Received24March2016
Accepted for publication7June2016
Published23November2016
Abstract
A new pellet injection system has been equipped on the experimental advanced superconducting
tokamak(EAST)in the2012campaign,with a pellet size of f2mm × 2mm,a frequency of
1Hz–10Hz and velocity of150m s?1–300m s?1.The deuterium pellet is well-known for
plasma fuelling as well as for triggering the edge localized mode(ELM).In the2012campaign,
pellet injection experiments were successfully carried out on EAST.Temporary plasma
detachment achieved by deuterium pellets has been observed in a double null(DN)divertor
con?guration,with multi-pellet injections at a repetition frequency of2Hz.The partial
detachment of the outer divertors and complete detachment of the inner divertors was achieved
after35ms of each pellet injection,which have a duration of30–60ms with the maximum
degree of detachment(DOD)reaching3.5and37,respectively.Meanwhile,the multifaceted
asymmetric radiation from the edge(MARFE)phenomena was also observed at the high?eld
side(HFS)near both the lower and upper X-points with radiation loss suddenly increased to
about15%–70%,which may be the main cause of divertor plasma detachment.The temporary
detachment induced by pellet injection may act as a new way to study divertor detachment
behaviors.
PACS numbers:52.55.Rk
1.Introduction
For many present tokamaks and next-step fusion devices,the heat and particle?uxes to the plasma material surface are of great importance in the determination of the lifetime of the plasma facing components(PFCs),especially the divertor targets.An operation in a partially detached mode for divertor tokamaks has been recognized as the most promising way,as it can greatly reduce the heat loads to divertor targets and enhance the lifetime of PFCs.Gas puf?ng and resonant magnetic perturbance(RMP)are thought to be useful approaches to obtain plasma detachment and have been stu-died for many years on ASDEX-Upgrade[1],JET[2]and so on.In this work,a new method towards plasma detachment triggered by pellet injection will be presented,which provides another way to investigate the divertor detachment behaviors.
Pellet injection is well known for plasma fueling[3]and ELM pacing[4,5],the latest results on typical phenomena
?2016Hefei Institutes of Physical Science,Chinese Academy of Sciences and IOP Publishing Printed in China and the UK Plasma Science and Technology Plasma Sci.Technol.19(2017)015101(7pp)doi:10.1088/1009-0630/19/1/015101
and related physics can be found in [6].In the2012cam-
paign,a new pellet injection system was equipped on the
EAST tokamak[7].The pellet injector,based on a screw
extruder,is able to?re pellets in the steady-state mode with a
reliability greater than95%.Typical phenomena such as ELM
triggering and electron temperature drop,which are asso-
ciated with deuterium pellet injection experiments,have been
observed and summarized in a previous work[8].This paper
mainly focuses on the temporary divertor plasma detachment
with MARFE events induced by pellet injection.For the rest
of this paper,the EAST tokamak and experimental setup for
pellet injection experiments are introduced in section2.
Section3gives the detailed information on divertor detach-
ment induced by pellets.A brief introduction of the obser-
vation of MARFE phenomena will be presented in section4.
Section5is the summary.
2.Experimental setup
EAST is the?rst fully superconducting tokamak to demon-
strate high-power,long-pulse operations with an ITER-like
con?guration in the world[9].It can be operated in limiter
and three divertor con?gurations,including upper single null (USN),double null(DN)and lower single null(LSN)divertor con?gurations.The purpose of its designation is to research
the physical issues of diverted tokamaks in steady-state
operations.The critical design parameters are major radius
R = 1.7–1.9m,minor radius a = 0.4–0.45m,maximum
plasma current I p = 1MA,maximum toroidal?eld B t = 3.5T,elongationκ = 1.9and triangularityδup to0.7. The experiments reported in this paper were carried out in the 2012campaign.In the2012campaign,EAST was equipped with a2.45GHz low hybrid wave(LHW)heating system with a heating power of2MW,ion cyclotron resonance fre-quency(ICRF)heating system of4.5MW with frequency ranging from20to100MHz.The PFCs were all upgraded to molybdenum except for two divertors,which still remained graphite.Lithium coating was applied to obtain proper wall conditioning with a relatively low ratio of hydrogen to deuterium.
The main diagnostics associated with this work are as
below.Divertor triple Langmuir probes arrays shown as ?gure1(a),which are embedded in the upper and lower divertor regions,can provide information on the electron density,electron temperature,heat and particle?uxes of the divertor region[10],also shown are the plasma separatrix for EAST#41873at6.54s and the location of low?eld side (LFS)pellet injection.Three multi-channel extreme ultra-violet(XUV)arrays(shown in?gure1(b)),can provide the line-averaged and total radiation intensity of both the core and edge regions.A set of re?ectometers is used to measure the outer mid-plane electron density pro?les.18channels CIII line emission(shown in?gure1(c))and three multi-channel H-alpha(D-alpha)radiation arrays(shown in?gure1(d)) are used,which are diagnostics relevant to radiation measurements.3.Plasma detachment induced by pellet injection
In the2012campaign,pellet injection experiments were
successfully performed on EAST.Plasma detachment has
been observed in several modulating L-mode discharges,
where a typical shot is41873.In this DN discharge,plasma
current I p = 400kA,toroidal?eld B t = 2T,and the heating power includes ohmic power and an additional auxiliary
ICRF power of about0.6MW.The deuterium pellets are
injected nine times from3.5s to7.5s with a time interval of Δt = 0.5s.
Plasma detachment is characterized by the low plasma
temperature at the divertor region,typically less than2eV,
and the low rates of heat and particle?uxes to the divertor
targets.In this work,plasma detachment is observed
through the sudden temperature drop at the divertor region
and decrease of heat and particle?uxes to the divertor
targets by using the divertor Langmuir triple probe diag-
nostics,as well as the remarkable increase of Dαsignal at
the divertor region.Figures2(a)and(b)are the2D contour
images of particle?uxes at upper outboard(UO)(a)and
upper inboard(UI)(b)divertors of41873.The particle ?uxes at the UO divertor are enormously enhanced at the onset of ICRF heating while the UI divertor shows no response.The two strike points move slowly toward opposite directions.Judging from the temperature drop at the inner and outer divertor targets(shown in?gures2(e)–(g))and the obvious changes of brightness after pellet injection,it is very clear that the UO divertor is partially detached while the UI divertor gets totally detached after about35ms of pellet injection with a remarkable increase of Dαsignal at the divertor region(?gure2(d)).The time traces of plasma stored energy shown in?gure2(c)indicate an improved con?nement mode may be induced by pellet injection.What is truly remarkable is that the plasma detachment can be modulated periodically by multi-pellet injections,which may provide a novel method to investi-gate the potential physics in divertor https://www.doczj.com/doc/aa9778990.html,-parison between particle?ux pro?les of pre and post injection phases with pellet injection at6.0s is shown in ?gure3.The pre-pellet injection pro?les at5.99s indicate that the divertor plasmas are attached with maximum par-ticle?uxes reaching1.6Acm?2and0.9Acm?2for UO and UI divertors respectively.The maximum particle?uxes on the outboard divertor are almost double of those on the inboard divertor,which may be caused by divertor asym-metry[11,12].The post-pellet injection pro?les at6.05s are marked by red https://www.doczj.com/doc/aa9778990.html,pared with the pre-pellet injection pro?les,the particle?uxes at both divertors are greatly decreased by pellet injection.The UO divertor showed partial detachment after pellet injection with par-ticle?uxes at strike point areas enormously reduced by a factor of9while a little enhanced at areas far away from the strike point;this interesting phenomenon indicates that the particle?ux pattern has been changed with particles transferred indirectly from near the strike point areas to the remote areas by pellet injection.The UI divertor,however,
is totally detached through all the target areas with almost no particles reaching the divertor.
To better illustrate the temporary divertor detachment in this case,a notion called the degree of detachment (DOD )is applied here,which is de ?ned to be the ratio of calculated (Φcalc )and measured (Φmeas )particle ?uxes to the targets [13].The calculated particle ?uxes reaching the targets,according to the two-point model [14],are pro-portional to the square of upstream separatrix density n sep .In this paper,edge plasma density at normalized radial location ρ = 0.98is applied to replace n sep due to the limited ability for the re ?ectometer on EAST to measure n sep .The density pro ?les beyond ρ = 1.0in ?gure 4(a )are the ?t lines.The measured particle ?uxes are the total particle ?uxes to the targets,which can be obtained by integrating all the divertor triple Langmuir probe data along
the divertor targets:
??????ò?f p p =′
G D ′D ′D ?′G D ′′
D +-D ++
+
r R r d r r R i r i r i 22112
1D
i probe D
meas ,()()
()()
()()()()
Here Δr is the distance from the strike point along the
divertor target,so the DOD can be calculated as:
j j j ==
′DOD k n 2calc
meas sep meas
12()()
In the attached regime,assuming no signi ?cant pressure
and energy loss along the SOL,we have Φcalc = Φmeas and DOD = 1.In the detached regime,Φmeas is signi ?cantly decreased,therefore Φcalc > Φmeas and DOD > 1.In
this
Figure 1.(a )The poloidal distributions of divertor tripe Langmuir probe arrays on EAST tokamak (2012).UI (O )-upper inboard (outboard )
divertor,LI (O )-lower inboard (outboard )divertor.Also shown are the plasma separatrix for EAST #41873at 6.54s and the location of low ?eld side (LFS )pellet injection.(b )Three multi-channel extreme ultra-violet (XUV )arrays.(c )18channels CIII line emission.(d )Three multi-channel H-alpha (D-alpha )radiation arrays.
case,plasma detachment by pellet injection is well con-?rmed by the dramatic increase of the DOD of the four targets after pellet injection.The distributions of DOD for the four targets are shown in ?gure 4.Figures 4(a )–(f )are outer mid-plane density pro ?les right before and after pellet injection at t = 6.5s from re ?ectometer (a ),time evolu-tions of DOD at UO (c ),UI (d ),LO (e )and LI (f )divertors as well as the enlarged view of DOD for UI target during t = 4.96–5.14s (b ).The deuterium pellets injected nine times from 3.5s to 7.5s with a time interval Δt = 0.5s.The DOD of the four targets remained 1until the DOD began to increase after about 30ms of each pellet injection with detachment durations of about 30–60ms.An excep-tion exists as there is no obvious reaction to the pellet injection at 4.5s.The deuterium pellet melted without causing enough perturbation to the plasmas,which may be the reason for this.From ?gure 4we can see that the maximum DOD for UO and LO divertors is about 3.5,while the LI divertor has a maximum DOD of about 15and the UI divertor,which is totally detached with maximum DOD reaching up to 37.The huge differences between the DOD of outboard and inboard divertors indicate that MARFE events induced by pellet injection may exist at HFS close to the X-points,which can cause a higher pro-portion of radiation power loss at areas near the inner divertors.
In addition,the heat ?uxes reaching the targets,which are closely related to the particle ?uxes at the divertor targets,are also sharply decreased by the pellets.Figure 5
demonstrates
Figure 2.(a )and (b )The 2D contour images of particle ?uxes at UO (a )and UI (b )divertor targets of shot 41873.(c )Time traces of pellet
injection waveform (red ),plasma stored energy (blue )and ICRF power (black ).(d )Channel 2U D αsignal evolution.(e ),(f )and (g )Temperature evolutions at UO and UI divertor targets and the enlarged view of temperature evolution for UI target during t = 4.97–5.17
s.
Figure 3.Particle ?ux pro ?les along the UO (a )and UI (b )divertor
target plates right before pellet injection (attached )and after pellet injection (detached ),mapped to the outer mid-plane with the equilibrium ?tting (EFIT )code.
the parallel heat ?ux pro ?les along the UO (a )and UI (b )divertor targets right before and after pellet injection.Just like the particle ?ux pro ?les,the pre-pellet injection pro ?les at 5.99s show that the divertor plasmas are attached with maximum parallel heat ?uxes reaching 1.65MW m ?2and 0.85MW m ?2for UO and UI divertors respectively,the maximum parallel heat ?uxes on the outboard divertor are almost doubled of those on the inboard divertor due to divertor asymmetry.The pro ?les marked by red triangles are the post-pellet injection pro ?les at 6.05s.Similar to the change of particle ?ux pro ?les,the parallel heat ?uxes of the UO divertor around the strike point areas are greatly reduced by a factor of 8.5while they remain almost unchanged far from the strike point areas.This may result from the change in the UO divertor particle pattern and may provide a new method to investigate the divertor detachment behaviors.The UI divertor,on the other hand,is totally detached with almost no heat ?uxes to the target.
4.Evidence of MARFE events
MARFE is a toroidally symmetric but poloidally asymmetric region of the main plasma close to the inner major radius [15].It is characterized by high density and radiation loss and often occurs together with plasma detachment.The formation of MARFE is considered to have something to do with the local thermal imbalance along the edge magnetic ?eld.In EAST shot 41873,MARFE phenomena are con ?rmed to be induced by pellet injection with a highly radiative region at HFS
close
Figure 4.The outer mid-plane density pro ?les right before and after pellet injection at t = 6.5s from re ?ectometer (a ),time evolutions of
DOD at UO (c ),UI (d ),LO (e )and LI (f )divertors as well as the enlarged view of DOD for UI target during t = 4.96–5.14s (b )
.
Figure 5.Parallel heat ?ux pro ?les along the UO (a )and UI (b )
divertor target plates right before pellet injection (attached )and after pellet injection (detached ),mapped to the outer mid-plane with the EFIT code.
to the X-points.Figure 6shows the modi ?cation of some signals after pellet injection and the density evolution.The signals of radiation intensity from XUV (d ),D α(e )and CIII line emission (f )are suddenly increased after about 30ms of pellet injection,which indicate MARFE events may be induced by the pellets.The stored energy is also increased by a factor of 1.2after about 50ms of the injection.This indi-cates an improved con ?nement mode may have been achieved by the MARFE events,which has also been observed in the HT-7tokamak [16].The core plasma line-averaged density evolution shown in ?gure 6(h )seems to indicate that the pellets have posed little in ?uence to the core plasma density.A similar conclusion can be made judging from the outer mid-plane density pro ?les (shown in ?gure 4(a ))right before and after pellet injection from the re ?ectometer.The density pro ?les show that the pellet has only affected the density at ρ= 0.965–1.0where ρis the normalized radial location.So the plasma detachment and MARFE phenomena may be induced by the increased edge plasma density caused by pellets.
Figure 7is the 2D contour images of line integrated radiation intensity from the XUV diagnostics.The region measured is located at the HFS close to the X-points.The times for pellet injection and crossing the LFS separatrix are shown in the picture with red and black lines,respectively.The radiated power remains at a low degree until after about 30ms of pellet injection at 6.5s,when there is a remarkable increase of radiation loss shown in ?gure 7.The MARFE events are obviously con ?rmed by the brightness of this area with a duration of about 8ms.The existence of highly
radiative areas at the HFS close to the two X-points may have resulted in the detachment of both of the two divertors,which has also been reported on JT-60U [17,18].Figure 8illustrates the total radiated power from the XUV diagnostics,the radiation loss suddenly increased about 15–70percent
by
Figure 6.Time traces of plasma current I p (a ),pellet injection signal (b ),plasma stored energy (c ),radiation intensity from XUV (d ),D αline
emission (e ),CIII line emission (f ),ICRF heating (g )and core plasma line-averaged density (h ).Also shown is the enlarged view of the XUV signal during t = 6.48–6.70s (i )
.
Figure 7.2D contour images of line integrated radiation intensity
from XUV.The measured region is located at HFS close to the X-points.The red and black lines are the time for pellet injection and crossing the outer mid-plane separatrix at 6.500s and 6.504s,respectively.
pellet injection.This should be reasonable as the radiation loss in HFS areas close to the X-points is dramatically increased by the existence of MARFE events.
5.Summary and conclusions
Pellet injection experiments were successfully performed on EAST.Temporary plasma detachment with MARFE events by pellet injections in the2012EAST campaign has been presented in this article.The deuterium pellet,which contains about3.78 × 1020atoms,caused suf?cient perturbation to the edge plasmas.The partial detachment of the outboard diver-tors and the complete detachment of the inboard divertors are obtained at the onset of MARFE and have a duration of about 30–60ms.MARFE events have been observed after about 30ms of pellet injections by radiation diagnostics.The ratio of the radiation loss to the energy across separatrix is sig-ni?cantly increased with the appearance of MARFE,which may be the direct reason for the plasma detachment.The plasma detachment achieved here,especially at the UO divertor target,is fairly interesting due to the changes in heat and particle patterns and may need more experiments and diagnostics to investigate the divertor detachment behaviors by pellet injection.So this may provide a different way to study divertor plasma detachment.
Acknowledgments
The authors are grateful to all members of the EAST team for their contributions to the experiments.This work was sup-ported by National Natural Science Foundation of China
(Nos.11575236,11275231,11305206)and the National Magnetic Con?nement Fusion Science Program of China
(Nos.2013GB107003,2014GB106005,2015GB101000). References
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407 Figure8.Total radiated power measured by XUV diagnostics.
2.1整式 第一课时:单项式教案 教学目标： 1、理解用字母可以表示任何有理数，初步认识用字母表示数的意义 2、掌握用含有字母的式子表示数的书写规定 3、理解单项式及其相关概念 4、利用单项式的概念求值 重点难点 重点：1、理解用字母可以表示任何有理数，初步认识用字母表示数的意义2、理解单项式及其相关概念 难点：1、掌握用含有字母的式子表示数的书写规定2、利用单项式的概念求值 教学设计： 一、创设情境 情境引入1、生活中的字母 情境引入2、2016年9月15日，中国在酒泉卫星发射中心用长征二号FT2火箭将天宫二号空间实验室发射升空.它在椭圆形轨道上环绕地球飞过1周，约需90分钟.请问： (1)绕地球飞行10周约需多少分钟？ (2)绕地球飞行n 周约需多少分钟？ 1、一件衣服的原价是q 元，打7折出售，现价是：（ ）元 2、《数学走向中考考场》单价是b 元，买了a 本，总价是（ ）元. 3、一块长方形菜地的面积是am 2，长是4米，宽是 （ ）米 4、一辆大卡车能载 54 1 吨的货物，t 辆车大卡车能载（ ）吨 5、一本笔记本5元，一只圆珠笔1元，买m 本笔记本，n 支圆珠笔，总价是（ ）元。 6、姚明个字高，经测量他通常跨一步的距离1米，若取向前为正，向后为负，那么姚明向前跨 a 步为 （ ）米，向后跨a 步为 （ ）米. 二、小组讨论，探索新知 活动一：讨论：用含有字母的式子表示数的书写有何规定？ 1、数和字母相乘，可省略乘号，并把数字写在字母的前面 2、字母和字母相乘，乘号可以省略不写或用“ · ” 表示. 一般情况下，按26个字母的顺序从左到右来写. 3、除法运算写成分数形式，即除号改为分数线 4、带分数与字母相乘时，带分数要写成假分数的形式 5、若式子后面有单位且式子是 和 或 差 的形式，式子应用括号 括起来。 6、数字因数是1或 -1 时，1常省略不写。如1a 写成 a ， -1a 写成-a
整式 ---单项式 教材分析 本节课得主要内容就是通过用字母表示简单得数量关系引出单项式及有关得概念,为进一步学习多项式、整式得加减做充分得准备。 学情分析: 在小学她们已经学习过用字母表示数,这对于她们进一步学习用字母表示简单得数量关系就是有帮助得,因此在教学过程中除了引导她们正确地用字母表示数量关系外,应把重点放在她们对单项式有关概念得理解与运用上,为整式得加减做准备。 教学目标: 知识与技能 1、了解代数式得概念,会列代数式表示简单得数量关系,掌握代数式得书写注意事项; 2、理解单项式得概念,掌握单项式得系数与次数得概念,能判断一个代数式就是不就是单项式,对于一个单项式能说出它得系数与次数。 过程与方法 1通过练习、合作探究用字母表示简单得数量关系, 2通过引导学生观察、发现、归纳及变式训练掌握单项式、单项式得系数与次数得概念。 情感态度与价值观 1通过观察、体验、运用,让学生经历探索数量关系与变化规律得过程,感受到用字母表示数得优越性。 2、在进一步理解用字母表示数量关系得过程中建立符号意识,激发学生学习数学得积极性。 教学重点难点及突破 1、本节课得直接目标就是让学生了解用字母表示数得概念,理解单项式有关得概念,能分清代数式中得那些就是单项式,并知道它们得系数与次数。 2、重难点得突破在于用字母表示数量关系及理解单项式有关得概念。 教学准备:多媒体课件 【教学设计】, 一、课前复习 前一段时间我们学习了有理数,但许多时候,我们不能用具体得数字来表示,却可以用字母来表示,那么这种表示方法有哪些呢?同学们,您们把下面得空填上给老师瞧瞧好吗? n只青蛙____张嘴,____只眼睛,____条腿,____声扑通跳下水。(打开ppt) 二、创设情境,引入新课 (幻灯片) (创设情境)举世瞩目得青藏铁路于2006年7月1日建成通车,实现了几代中国人梦寐以求得愿望,青藏铁路就是世界上海拔最高、线路最长得高原铁路。 (情境问题)青藏铁路线上,在格尔木到拉萨之间有一段很长得冻土地段,列车在冻土地段得行驶速度就是100千米/时,在非冻土地段得行驶速度可以达到120
单项式乘以单项式教学设计 一、教学目标 1．知识与技能 使学生理解单项式乘法法则，会进行单项式的乘法运算。 2．过程与方法 通过单项式乘法法则的推导，发展学生的逻辑思维能力。 3. 情感态度价值观 让学生主动参与探究，形成独立思考、勇于探究的习惯。 二、教学重点、难点： 重点：掌握单项式乘法法则。 （这是因为要熟练地进行单项式的乘法运算，就得掌握和深刻理解运算法则，对运算法则理解得越深，运算才能掌握的越好） 难点：单项式乘法法则有关系数和指数在计算中的不同规定（这是因为单项式的乘法最终将转化为有理数的乘法、同底数的幂相乘、幂的乘方、积的乘方等运算，对于初学者来说，由于难于正确辨认和区别各种不同的运算及运算所使用的法则，易于将各种法则混淆，造成运算结果错误。） 三、教学过程 1、创设情境，导入新课 引入课本中的问题2： 光的速度约为3 X105千米/秒，太阳光照射到地球上需要的时间大约
是5 X102秒，你知道地球与太阳的距离约是多少千米吗？分析：距离二速度X时间；即(3X105 )X(5 X102 ); (1)怎样计算(3 X105 ) X(5 X102 ) ? (3X105)X(5X102) =(3 X5) X(105 X102) =15 X10 7 =1.5 X108 (千米) (2)如果将上式中的数字改为字母，比如ac5?bc5，怎样计算这个式子。 ac5?bc5是单项式ac5与be5相乘，我们可以利用乘法交换律、乘法结合律及同底数幂的运算性质来计算。 让学生回忆上学期单项式有关问题以及有关幂的运算来引入课题，以培养学生学习前后知识的连续性、一致性，由浅到深，循序渐渐，提高学生的学习兴趣，明确本节课的学习内容。 2、思考探索 2 5 3 2 通过计算4a2x5? 3a 3bx2，总结单项式乘以单项式的运算法则：单项式与单项式相乘，把它们的系数、同底数幂分别相乘，对于只在一个单项式里含有的字母，则连同它的指数作为积的一个因式。
人教版七年级数学上册第二章第一节 《单项式》 教学设计
2.1 《单项式》教学设计 涉县第三中学赵云平 一、教学目标 （一）知识目标 (1) 理解单项式及单项式系数、次数的概念。 (2) 会准确迅速地确定一个单项式的系数和次数。 （二）能力目标 (1) 初步培养学生观察、分析、抽象、概括等思维能力和应用意识。 (2) 通过讨论、提问等方式，经历概念的形成过程，培养学生自主探索知识和合作交流能力。 （三）德育目标 （1）激发学习的内在动机； （2）养成良好的学习习惯。 二、教学重点和难点及教学设计要点： （一）教学重点：掌握单项式及单项式的系数、次数的概念，并会准确迅速地确定一个单项式的系数和次数。 （二）教学难点：单项式概念的建立。 （三）教学设计要点：为突出重点，突破难点，教学中要为学生提供足够的感知材料，丰富学生的感性认识，帮助学生认识概念，同时在剖析单项式结构时，借助反例练习，抓住概念易混淆处和判断易出错处，强化认识，帮助学生理解单项式系数、次数，为进一步学习新知做好铺垫。 三、教学方法： 分层次教学，讲授、练习相结合。 四、课型 新授课 五、教学工具 投影仪，复印课堂作业设计每学生各一份 六、教学过程： 一、复习引入： 1、由《数青蛙》儿歌引入课题，学生积极性较高: 2、用含有字母的式子填空: (1)边长为a的正方体的表面积为,体积为； (2)铅笔的单价是x元，圆珠笔的单价是铅笔单价的2.5倍，圆珠笔的单价是元； (3)全校学生总数是m,其中女生占总数48﹪，则男生人数是； (4)一辆汽车的速度是v千米/时，它t小时行驶的路程为； (5)数n的相反数是。
整式的乘法（二） 单项式乘以多项式（教案） 学习目标 1．在具体情景中，了解单项式乘以多项式的意义，理解单项式与多项式的乘法法则； 2．能熟练、正确地运用法则进行单项式与多项式的乘法运算. 3．经历探索乘法运算法则的过程，让学生体验从“特殊”到“一般”的分析问题的方法，感受“转化思想”、“数形结合思想”，发展观察、归纳、猜测、验证等能力. 4．初步学会从数学角度提出问题，运用所学知识解决问题，发展应用意识.通过反思,获得解决问题的经验.发展有条理的思考及语言表达能力. 学习重点：在经历法则的探究过程中，深刻理解法则从而熟练地运用法则. 学习难点：正确判断单项式与多项式相乘的积的符号. 学习过程： 一、复习回顾 1、单项式与单项式怎样相乘. 单项式与单项式相乘，把它们的系数、相同字母分别相乘，对于只在一个单项式里含有的字母，则连同它的指数作为积的一个因式.
2、单项式与单项式怎样相乘运用了哪些乘法运算律？除此之外，还有什么乘法运算律? 单项式与单项式相乘运用了乘法交换律、结合律， 一、联系生活设境激趣 问题一：1.在一次绿色环保活动中购买奖品如下表, ⑴有几种算法计算共花了多少钱？⑵各种算法之间有什么联系？ 请列式：方法1: ; 方法2： . 联系……① 2．将等式15(5.20+3.40+0.70) =15×5.20+15×3.40+15×0.70 中的数字用字母代替也可得到等式：m（a+b+c） =ma+mb+mc；……② 问题二：三家连锁店以相同的价格m (单位:元/瓶) 销售某种商品,它们在一个月内的销售量(单位:瓶) 分别是a,b,c。你能用不同的方法计算它们在这个月内销售这种商品的总收入吗? 方法一：先求三家连锁店的总销量，再求总收入，即 总收入（单位：元）为：m(a+b+c) 方法二：先分别求三家连锁店的收入，再求它们的和，
2.1整式---多项式 教学内容： 教科书第56—59页，2.1整式：2．多项式。 教学目标和要求： 1．通过本节课的学习，使学生掌握整式多项式的项及其次数、常数项的概念。 2．通过小组讨论、合作交流，让学生经历新知的形成过程，培养比较、分析、归纳的能力。由单项式与多项式归纳出整式，这样更有利于学生把握概念的内涵与外延，有利于学生知识的迁移和知识结构体系的更新。 3．初步体会类比和逆向思维的数学思想。 教学重点和难点： 重点：掌握整式及多项式的有关概念，掌握多项式的定义、多项式的项和次数，以及常数项等概念。 难点：多项式的次数。 教学方法： 分层次教学，讲授、练习相结合。 教学过程： 一、旧知复习 1、练习巩固 复习提问：什么是单项式、系数、次数？ 二、讲授新课： 创设情境：1、小明房间的窗户如图所示，其中上方的装饰物由两个四分之一圆和一个半圆组成（它们的半径相同）（1）装饰物所占的面积是多少？（2）窗户能射进阳光部分的面积是多少？（让学生讨论） 2、填空 （1）一个数比数x的2倍小3，则这个数为____; （2）如图1，三角板的面积为____； (3)买一个篮球需要x元，买一个排球需要y元买一个足球需要40元，买3个篮球、5个排球、2个足球共需要元；
得出结果让学生观察 (由学生小组派代表回答，教师应肯定每一位学生说出的特点，培养学生观察、比较、归纳的能力，同时又锻炼他们的口表能力。通过特征的讲述，由学生自己归纳出多项式的定义，教室可给予适当的提示及补充。) 3多项式： 板书由学生自己归纳得出的多项式概念。上面这些代数式都是由几个单项式相加而成的。像这样，几个单项式的和叫做多项式。 在多项式中，每个单项式叫做多项式的项其中，不含字母的项，叫做常数项 一个多项式含有几项，就叫几项式。多项式里，次数最高项的次数，就是这个多项式的次数。 注意： (1)多项式的次数不是所有项的次数之和； (2)多项式的每一项都包括它前面的符号。 (教师介绍多项式的项和次数、以及常数项等概念，并让学生比较多项式的次数与单项式的次数的区别与联系，渗透类比的数学思想。) 2．例题： 例1：判断： ①多项式a 3－a 2ｂ＋a b 2－b 3的项为a 3、a 2ｂ、a b 2、b 3，次数为12； ②多项式3n 4－2n 2＋1的次数为4，常数项为1。 (这两个判断能使学生清楚的理解多项式中项和次数的概念，第(1)题中第二、四项应为 －a 2b 、－b 3，而往往很多同学都认为是a 2b 和b 3，不把符号包括在项中。另外也有同学认为该多项式的次数为12，应注意：多项式的次数为最高次项的次数。) 例2：指出下列多项式的项和次数： (1)3x －1＋3x 2；(2)4x 3＋2x －2y 2。 解：略。 例3：指出下列多项式是几次几项式。 (1)x 3－x ＋1；(2)x 3－2x 2y 2＋3y 2。 3540x y ++23x -2 12 ab r π-216ab b π -
整式的乘法 单项式与单项式相乘 教学内容：冀教版七年级下册10.4 整式的乘法第一课时 教学目标： 知识与技能 理解并掌握单项式与单项式相乘的法则，能够熟练 地进行单项式的乘法计算。 过程与方法 经历单项式与单项式相乘的法则的探究过程，培养 学生的归纳、归纳、猜测、验证等能力． 情感态度与价值观 在单项式与单项式相乘的计算过程中培养学 生认真细心的作风． 教学重点：．对单项式运算法则的理解和应用。 教学难点：尝试与探究单项式与单项式的乘法运算规律。 教学方法：尝试教学法 教学用具：多媒体课件、投影仪、导学案 课时安排：一课时 教学过程： 一、准备尝试：（查漏补缺，学生分组采用记分制，比一比哪一组得 分最高） 1、指出下列公式的名称 指名学生回答。 2、只要认真，你就能全部计算正确，看谁一遍全部正确。 （1） （2） （3） n m n m a a a +=?mn n m a a =)(n n n b a ab =)(35x x ?3b b ?2 a a a ??
（4） （5） （6） （7） （8） 3、单项式中的数字因数叫做这个单项式的__________ 4、你能说出下列单项式的系数吗？ －4x 2 y (－2x 2y)2 5、利用乘法交换律、结合律计算： 二、创设情境，导入新课： 1、现有长为x 米，宽为a 米的矩形，其面积为多少平方米？ 2、长为x 米，宽为2a 米的矩形，面积为多少平方米？ 3、长为2x 米，宽为3a 米的矩形，面积为多少平方米？ 启发思考：在这里，求矩形的面积，会遇到223a x x a x a ???， 这是什么运算呢？ 导入新课： 因式都是单项式，它们相乘，就是我们今天要学习的“单项式与单项式相乘”。 出示课题和教学目标。 三、出示尝试题： 1、尝试把上面的计算表示成更简单的结果。 (1)a x ax ?= (2)22x a ax ?= (3)236x a ax ?= 2)(a -32)(a -3 23)(y x 2 32a a a ??)(25n m 5351b a -= ???251346m m ?-4)(